What TM was stating was that if the STATE (i.e., the prosecution) requests a jury, they can have it even if the defense doesn't. The US Constitution (and many of the states) guarantees the right of the defendant to a jury trial, but it is unspecified if the state has the same right. However, there are court cases (notably the Illinois Supreme Court People v. Scornavache) that do give such right to the state.
In Ohio, if the defendant demands a jury trial, the state has to abide by it. The exception is Minor Misdemeanor charges, they are not triable by Jury.

