In Kentucky, they'll send (usually) 3 state troopers, and knock on your door. If the person that they want isn't at home, they'll take your word for it, and let you be on your way.
In Ohio, it's usually six or more officers with guns drawn. They'll try to open the doors of the house to gain entry without knocking or announcing their presence. When the person that they're looking for isn't at home, they'll try to find a reason to come inside and search the property looking for that person (and a reason to arrest everyone inside). They'll then circle the house outside for 24-48 hours to intimidate the people inside but eventually give up when they realize that the person doesn't actually live there.
What's really sad is that I was great friends with a member of Law Enforcement until I realized how short-sighted and two-faced he was; the LEO community really breeds an environment of "us versus them" and if you're a defendant (regardless of guilt or innocence), you're a scumbag who deserves to be in jail.