Can the police search you, your car, or your premises? It depends.
One thing it depends on is if you consent. The US Supreme Court has instructed us that a consentual search is always legal. So lesson number one, if the police ask to search you, under no circumstances should you say yes.
Another thing it depends on is if they have probable cause to arrest you. If they do, then a search is allowed as being incident to arrest. Whatever they find can be used against you.