If planning to move, ORC 5321.17 requires that:
A tenant
with a month-to-month agreement provide the landlord with at
least thirty (30) days notice before the next rent due date.
EXAMPLE: If rent is due on the first of the month then the tenancy will terminate on the last day of the month. If the tenant gives the landlord notice on September 4th that the tenant is moving, the tenancy will not be terminated until October 31st.
If you have a written rental agreement, you need to check that agreement to see what your obligations are to properly terminate your tenancy.
ORC 5321.16(B):
Obligates the landlord to:
Return the security
deposit and/or a written itemization of any deductions from the
security deposit within thirty (30) days of the tenant
terminating the rental agreement and moving out.
ORC 5321.16(B)
also states that:
The tenant shall provide the landlord written
notice of the address to which the security deposit is to be
sent. If the landlord does not return the security deposit
within 30 days, or the tenant disagrees with the amount returned,
the tenant may sue for double the amount wrongfully withheld and
reasonable attorney's fees.