Don't take this as bona fide legal advice, but the only way I've ever been able to ask a tennant to move within that time frame (3 day notice) was when my tennants were in violation of the lease and were not taking steps to become back in compliance with the lease. A three day notice to vacate has to be consipiciously posted on the property and that if the tennant does not move out within those 3 days, an eviction request will be filed (Forcible Entry and Detainer). A court date set and if the court agrees with the landlord and the court sets a move out date....
THIS IS NOT LEGAL ADVICE.... you should consult a legal professional for that. Googling Ohio Tennant Landlord Law should provide you with some helpful links
Scott Baker, Realtor
ERA Real Solutions