Thank you to all who answered my question last week about entering the premesis when the tenant has apparently moved out. When we inspected the property, it turned out that she was very obviously not living there (no furniture or clothing), but had left some other personal property (including two live fish in a tank). We sent a three-day eviction notice by certified mail to what we are pretty sure is her new address. We really would rather not go to court, though, so we also included a letter that she could sign stating that she wanted to terminate our lease effective immediately and that she "relinquishes possession of any objects left in or on the premesis after [insert date]", and that "any such objects are considered to be trash, and may be disposed of at the landlords discretion." If she actually does sign and return this letter to us, can we get rid of her stuff? Would the letter "hold up" in court if she decided later that she wanted to sue us for destruction of property? Also, can I call the ASPCA about the fish?
I know that I could just terminate the lease, with 30 days notice, and then store her belongings for 30 days, but we really need to get the place cleaned up and re-rented ASAP.
Also, I hope I haven't broken any laws by suggesting that she terminate the lease herself rather than end up with a court date for eviction... I couldn't find anything about this in Ohio's Landlord/tenant Code.
Any info would be greatly appreciated.

You should be able to mutually agree, in writing, to the terms you've just specified. Regarding the fish, your best bet is to just keep them yourselves or give them to someone you know who has an aquarium.