So, your detective, victim, or even murderer is going to claim self defense in Ohio. Here's what you need to know about Ohio legal self defense. In general, it's easier to give your character a lawyer, and even then you still have to know the laws. Always get a lawyer, in real life.
In public places
The thing to remember is that if you are in public places you have a duty to retreat, which means it is only legal if you couldn't retreat/avoid the danger and you believed fully that you were in danger (whether you actually were or not). If you believed you would be bodily harmed and couldn't escape, you have a right to self defense. That said, a jury still has to believe you. You are supposed to find a peace officer, if you can retreat. Also, if you caused the fight to begin with, you have no legal right to self defense.
In you (or your family's) home or car
There is something called the Castle Doctrine in Ohio. An intruder comes in and threatens you or your family and you have every right to shoot them in self defense. No duty to retreat exist in these places. There are loopholes that make this doctrine null, however. Also, if you are trespassing and commit a self defense you are illegally acting.
a. You invited the person you shot in, or a fellow resident did
b. they are a postal worker and have temporary right to be there
c. they are only peering in
d. they are leaving your home
e. they are a fellow resident of the home
There are several situations that would cause problems for a character in the way of legal self defense. You can create so many legal problems for your characters just by using the list of ways Castle Doctrine doesn't cover someone. For example, you invite your date in, they attack, you kill them in defense of your body, and you can't legally claim self defense. That's just one example.
Have fun putting your characters in bad legal situations and giving murderers ways to murder someone! Comment below if you want to know about something specific.