Okay, but keep in mind there are several pieces of paper you need.
1)Death Certificate. Shows the official dates of death. Shows the official cause of death. May also show address where found, family doctor's name if known, her last known address. Coroner may ask for that.
2)Autopsy report. Official findings of the body at the time the autopsy was completed.
3)Missing persons reports, if any were filed.
4)Police reports, investigative reports. Notes, witnesses interviews (they may not let you see those).
One thing to note is like Richard mentioned. In Ohio, the State Patrol is only thought to have jurisdiction on the highway. Actually, the have jurisdiction over the local police and sheriff's dept. in investigation of those depts. And they do frequently give assistance to local LE agencies, and they have to document everything they do. So they may have some info.
Don't be afraid to go to the courthouse to look for info. Most of what is in the courthouse is public info and searching there is easy to do. You can ofen even see the court file if you specifically ask for it. Just go to probate office, tell them what you want to find and ask them how you go about searching for it.
No, I never did anything with missing people. LOL, I just read a lot! And I have had a little personal experience researching info for a civil case. Got birth certificates for my kids, etc.
Info for obtaining a death certificate:
http://www.odh.state.oh.us/vitalstatistics/vitalstats.aspx
They always list an offical date of death. The exact date may not be known, but they have some policy on what date to use.