YES, BUT ONLY WITH YOUR CONSENT
Yes, it is perfectly legal for a cop to enter your house without permission to pursue a fugitive. It is also perfectly legal for them to do the same if they feel their is a potential danger inside. For instance, in the case of a fire.... they can ram down your door and drag you out kicking and screaming.
possession is 9/10's of the law. The question is, why was someone searching your home? Did they have a warrant? Did you open the door? No cop is searching my house without a very explicit warrant. KNOW YOUR RIGHTS!
no he needs a search warrant
As is often the case with analyzing the legality of an action taken by a cop, whether the cop can "just open your door" depends on the specific circumstances. For example, a cop can open your door when the cop has observed a felony in progress by seeing it through a window. Or when the cop is in hot pursuit of someone the cop has observed entering the dwelling. Otherwise, the general rule is that the cop must have a warrant before entering a dwelling without permission, and even with a warrant the cop usually must knock first and request admission (although not if the cop has a "no knock" warrant).
It depends on why he is entering. Was he called to the residence? Is he or she doing a 'welfare check'? What type of call history has there been at that residence? If the police officer has an arrest warrant, and knows the person named in the warrant is in the residence, then in the state of NC, the answer is yes.
They must provide a judge with probable cause to do a search.
a cop and/or a judge out of his/her files
i need to know what a cop needs to know in order to get a search warrent
No a representative of the law can not search your house if they do not have permission from the owner of property or a proper search warrant which only a judge can issue. If the officer did so he or she would be breaking amendment number 4 "search and seizers" which is illegal for even them to do.
Probably, yes.
not if you let him search it
If the cop has a warrant or if he thinks you stole something or if the cop thinks you have a weapon in a place you are not suppose to have the weapon.