If you are arrested in your home, officers may conduct a limited search of the immediate area where you are arrested without a search warrant. They may also check the rest of the house for any accomplices. They may seize any contraband, stolen property, or evidence of a crime discovered in plain view in any portion of the house where the officers have a right to be.
When you are arrested while driving your automobile, the officers may make a limited search of your car at that time for the purpose of discovering weapons that might be used against them. They may not make a general search of your automobile unless there is independent probable cause that the vehicle is carrying evidence of crime or contraband. If your vehicle is impounded, officers may conduct an inventory search before the vehicle is towed.
If a search is requested by an officer, you are not required to give consent. A consent to search will usually remove any claim you may have that a search was illegal.