It's (almost) never in your best interest to talk to the police. "Anything you say can and will be used against you." Invoke the 5th, then remain silent. You should also know your state's laws about identifying yourself. In my state, you must produce your id when pulled over operating a vehicle, but otherwise you're not required to id yourself. You don't have to let them enter your home without a warrant, either.
@wheresyourshoe in situations where the exigency clause is applicable such as a health checkup, you may have to let them into your home as you no longer have the 4th amendment protections against unreasonable/warrantless searches and seizures.
It's obviously circumstantial, but if you're not doing anything wrong they shouldn't have a reason to come in. Some cops will make up reasons, or might think a health check is enough reason. It all depends. They do need to believe someone is in danger inside your home. I've been welfare checked, and they didn't even ask to come in. I talked to them on my front steps.