Can they search my car after they tow it?

Yes, but both conditions matter, and each is a separate challenge.

Was the impound lawful? Not every arrest justifies towing. Where a licensed driver was present who could have taken the vehicle, where the car was legally parked on private property, or where department policy didn't call for a tow, the impound itself is attackable — and if it fails, the inventory that followed goes with it.

Did the search follow policy? Standardized procedures govern what gets opened. Officers who open sealed containers the policy doesn't cover, or who inventory selectively, have exceeded the exception.

A pattern worth noting: where the record shows the tow decision was made in order to enable a search, courts treat that differently than a genuine impound. What the officers said to each other at the scene, captured on body cam, sometimes answers that directly.