Do the police have a right to come into your house? Say you’re at home watching television when a police car pulls into the driveway. The officer walks up, knocks and tells you through the door that they’re there on official police business, and they want to come in and have a look around. Are you obligated to let them do it?
You certainly are not. They need to have a warrant, or in some cases, probable cause to believe that immediate entry is needed. For instance, an officer who is chasing someone who just robbed a bank does not have to go get a warrant if the bank robber runs inside their house.
In your case, though, where it is clear that a crime is not happening at the moment, it’s the warrant that is important. If you consent to a search, they can look around without it. If you tell them that you do not consent, though, they can’t come in. You can just yell it through the door if you don’t want to risk opening it and allowing them to see in your home. Many people will put the chain lock across the door and talk through the crack. Others will go out a back door, walk around to the front, and talk to the officer outside.
No matter what you choose to do, just remember that the officer cannot force an entry without a warrant. They should be able to show it to you if they claim that they have one. If they enter illegally and it leads to an arrest, it can have a drastic impact on your legal options.