You would think that the answer is simple, but it depends.
If the mortgage is:
(i) part of a "consumer credit loan", then 1 year [see ORC §1109.69 (A)(1)(h)];
(ii) not part of a "consumer credit loan", then 6 years [see ORC §1109.69 (A)(2)(e)]; BUT
If the OH superintendent of financial institutions designated a retention period specifically for paid off mortgage loans [see ORC §1109.69 (B)], then the retention period can be either 1 or 6 years.
If the superintendent made such a designation, it would be in the Ohio Administrative Code, which can be accessed at:
http://onlinedocs.andersonpublishing.com/oac/The safe answer is to keep it for 6 years, but that might take up a lot of unnecessary storage space. If you find the precise answer, please post so all can see.