"If a police officer searched a person's home without a warrant and didn't have the owner's permission, which Supreme Court case would the officer likely be violating"

Mapp v. Ohio.

In 1961 the US Supreme Court ruled (6-3) that evidence obtained in violation of the Fourth Amendment of the US Constitution, which prohibits "unreasonable searches and seizures," is inadmissible in state courts.

Hope this helps.

answer; pluralist democracy;