Can police come into your house without a physical arrest warrant in Ohio to arrest someone living there?

What does the questioner mean by having the "physical" arrest warrant?

If it means that, even though there is an existing warrant, but they just don't happen to have it in their possession - for them to act on the knowledge that the warrant exists is still lawful. They do not need to have the actual warrant in their possession in order to act on it.

As in most cases involving the law, the CIRCUMSTANCES of the situation dictate what law enforcement can, and should not do. For example;

If the police are in 'fresh pursuit' of someone and they run into the house they CAN pursue and arrest the individual inside.

If they knock on your door - you open it - and behind you, they see the wanted individual sitting in your living room, they can enter and effect the arrest.