That depends on the circumstances such as: what is the person charged with? Did they see them go into the home?? Why do they think the person is there?
If the police are in hot pursuit of a person or if they have a warrant for the arrest of a person and have good cause to think that person is in your home they do not need permission to enter and search for the person.
There are rules and circumstances under which they can enter. The person they were after might be able to raise illegal search in his defense, depending upon the actual facts.
No, the police do not have the right to enter your home without your permission and without a warrant. However, there is a question of what will happen to the police if the ignore you wishes. You may file a complaint with their superiors, but the officers in question probably won't suffer in the long term. Your friend might have a slightly better court case.
The 4th Amendment proscribes unreasonable searches and seizures. The procedure is to get a search warrant. Get all the official information, including police report, to see how they justify entering your home. Do online research. If you want to pursue it complain to the right person in the police dept./DAs office.
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