It appears from your fact pattern that the police must obtain a warrant to conduct the search. The police can always ask for your consent to search the vehicle (or anything), and the police do not need to make a threshold evidentiary showing in order to ask for consent to search.
You thus would also have a right - the right to decline to give your consent to the search. Good luck!
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They can ask. You can say no.
Otherwise, they'll need a warrant or probable cause.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.