Police can search your car if they are on patrol just for security measure. However, they are not legally allowed to search your house without a search warrant. If this should happen you are supposed to report to the head office. For any search, they must show probable cause.
IF they had a warrant signed by a judge--I wouldn't JUST let them search it IF you have something to hide---if you do NOT have something to hide, let 'em search away, will look better for YOU in the long run...but that is just in my opinion (IMO)
Dude, they have their eye on your or someone you know!!! Yes if they have probable cause to believe you are involved in something illegal they can stop you. Searches are different. They need a warrent to search your house and can only search you car without one if they find suspicious things on your person or see something in plain sight first.
Have they told you what they're searching for? Seems like harassment, to search your home they need a warrant unless you give them permission. In order for them to search the home without your permission they need a warrant, to get warrant they have to have evidence of some sort to get a judge to approve a warrant. If you've done nothing and you're clean then I'd refuse to allow them searches and make em work for a warrant.
Never let them search without a warrant, for instance if you bought the car used the old owner could have stashed something in it or a not so nice friend could have as well. In any case just do not let them without a warrant, they might consider anything a weapon.