There is nothing illegal about falling asleep in your car. In fact, it could be argued that society has an interest in intoxicated people sleeping in their cars rather than driving them.
But there are cases where this can amount to Reasonable Suspicion for the police to wake you up with a Terry stop. In a case where a driver fell asleep in his car while in a bank drive through lane, this was held to amount to Reasonable Suspicion for a stop. Bucyrus v. Lewis (1990), 66 Ohio App.3d 256.
But consider the location. Certainly, the guy did not drive sober to a bank drive through teller lane, get out, get drunk, then come back and sleep in his car. Rather, the more likely scenario was that the guy was driving drunk, felt he needed to stop off and get some money, and then while doing so, fell asleep waiting for his cash.
But if the location were different, say in the bar parking lot, it is entirely possible, even likely, that the guy came out of the bar drunk, got in his car, and fell asleep. While the police may have other justifications for approaching a person in such a situation (the so-called “community caretaking function”) wherein the police have a duty to render aid to the unconscious that might get them past not having reasonable suspicion, it will still be a hard case for the prosecutor to show that the vehicle was actually operated while the person was intoxicated.