What to do
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As the owner or resident of the house, you have the right to not let them in your house, unless they show you a warrant with information pertaining to you. Until a warrant is presented, you are allowed to not let them in.
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You do not even need to open the door. You can ask the officer to show the warrant through a window or put it under the door.
What you can do
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Again, the phrase "you have the right to remain silent" applies here as well. You have the right to not answer any questions or even talk to the police officers, when they are in your house.
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However, much like the last situation, do everything the office tells you to do, as this avoids any complications and further problems/consequences.
What the officer can do
As mentioned before, if the police officer shows you a warrant that has information pertaining to you and it is signed by a judicial officer, they have every right to completely search your house and move everything.