I would suggest you cover your arse and spend the small amount of money to insure the release is filed with the courthouse. I do not deal with Trumball County, but seriously doubt it will cost more than $5.00 to file.
If you go to the recorder they could tell you if a release was filed. May even be able to get them to do it over the phone.
In a word......YES!!!
The previuos posters have given you good information...whatever it takes, make certain it gets filed!