Question
I went to the mikva on Shabbos morning and before I left, I folded my towel neatly and placed it on the left side of the bottom shelf of a small closet in the mikva. When I returned Sunday morning there was no towel where I had placed my towel but on the right side of the top shelf in this closet there was a towel that was unfolded, and that looked exactly like my towel. I can't be sure that it is mine since there are no identifying features on the towel and there were none on my towel. Can I nevertheless assume that the towel that I saw is mine and take it? Since this is a public place, one cannot leave his towel indefinitely since the cleaning workers dispose of objects which are left on the premises, at random times.
Answer
We should preface that, as you noted, when one finds an object that he does not know if it is his, he must consider whether there are identifying features-simanim. The reason this is a crucial issue is that the Gemoro says that one can assume that a person who loses an object that does not have any identifying features, loses hope. He is misya'esh that he will be able to reclaim his object. After the owner is misya'esh from his lost object, the Torah states that anyone may take possession of the object.
Even though there are no simanim on the towel itself, it is possible that the owner has a siman. We rule (CM 262, 9) that generally location is a siman for objects that were originally put in a specific place. For example, if you had found the towel exactly where you left it, you would have assumed the towel was yours. This assumption is correct because in that case you had a siman and could therefore assume that the towel is yours. Similarly, if someone comes and tells you that he left his towel unfolded on the right side of the upper shelf you would need to give him the towel because he has a siman of place.
The Gemoro (BM 23B) says that sometimes place is not a siman. The case the Gemoro gives is when one finds an object in a place that many people leave this type of object. The example that the Gemoro gives is finding a barrel of wine in a dock area. Since many boats unload the barrels of wine that they transport there, the fact that a person states that he left a barrel of wine in the dock area is not a siman for a barrel of wine that was found because many people leave barrels of wine in this place. Moreover, according to many including Rashi, according to the second approach of the Gemoro even if a person is able to pinpoint the exact location where the barrel was found, place is still not a siman. Some poskim maintain that this is the authoritative approach.
This second approach does not apply in your situation. The Yad Dovid (ibid.) explains that the reason even pinpointing the exact location is not a siman according to this approach, is because since many people place this type of object in this place, one who places an object there has no hope of recovering his object. However, in your situation only a few people place towels in the closet and people do not usually move other people's towels. Therefore, according to all opinions knowledge of the precise place is a siman and we cannot assume that one who places his towel there gives up hope of recovering his towel. (You certainly expected to get your towel back.)
However, since the only siman you have is that you placed your towel in this closet and many people leave their towels there you do not have a siman. Another person may have a siman if he can tell the exact place he left his towel and it is the place where you found the towel. Thus, for you the place you found the towel is like finding wine at the dock. But for a person who can identify the exact place you found the towel, it is not like wine at the dock. The fact that generally a towel in a mikva is like wine at the dock is stated explicitly by the Minchas Yitzchok (3, 17).
Several modern-day poskim discussed cases that are similar to your case. The Minchas Yitzchok was asked whether a person who left a towel in the mikva and after two days found an identical towel in the mikva may take the towel that he found. He ruled that he may take it and wait for a while. If no one claims that he lost a towel he can keep the towel. Even though he does not state this, it seems that he requires the one who found the towel to put up a sign since otherwise no one will know whom to tell that he lost a towel in order to claim his lost towel.
The basis for his ruling is a ruling of the Taz (siman 136) in the case of a gentile lady who cleaned the clothes of several Jewish residents of a town and gave one of her customers a sheet that was definitely not his, but he had given her a different sheet to clean. The Terumas Hadeshen ruled that the one who received the sheet may not keep it since perhaps the true owner of the sheet did not yet despair of recovering his lost sheet. Therefore, it still belonged to him. The Taz writes that the Terumas Hadeshen agrees that if the one who received the sheet waits a while and does not hear that anyone is looking for a lost sheet, then the one who received the sheet may keep what he received because he can assume that the true owner is no longer interested in recovering his sheet. He suggests that a reason why he may no longer be interested is because he received compensation from the cleaner.
The Minchas Yitzchok maintains that even those who disagree with the Taz's ruling in that case agree in this case since it is possible that the towel that he found really is his, whereas, in the case of the Terumas Hadeshen it certainly was not his sheet.
The Even Yisroeil (8, 96) rules that even if one does not wait after he took the object that he found in the mikva, he still may keep it if is identical to the object he lost. His rationale is that there is no reason to believe that another person lost the same object as what he lost. Furthermore, he says that even if it turns out that the article that he found is not the one he lost, it is plausible that the owner of the object that he found does not mind the exchange.
The Pischei Choshen (Aveido 3, note 53) also rules that one who lost an identical object may take it and keep it without posting any notice. His reason is because since the object does not have a siman he may take it for himself. His rationale is that even if the loser realizes that he lost the object, he will give up hope since he does not have a siman. Moreover, even if the loser did not yet notice that he lost his object the finder may keep what he found because 1] perhaps it is his, and 2] even if it is not his, no one else will be able to claim that it is his, Therefore, the finder may keep what he found.
In your situation the argument of the Pischei Choshen does not apply because there is the possibility that someone will claim that he left his towel in the exact place that you found the towel. Thus, he has a siman. However, the argument of the Even Yisroeil does apply since people don't usually steal towels in the mikva so it is unlikely that someone took your towel and a third person forgot his towel in the same closet where you placed your towel.
The approach of the Minchas Yitzchok does work for you. That is, you can take the towel and put up a notice that you found a towel in the mikva without saying where you found it and wait a week. If no one comes and tells you that he left it in the place where you found it, you may keep it.
