

No, of course not! But, I do believe they would have done that anyway given that it was how the money was transported.
He arrived at the home, talked to LE there, told him his part (exactly how much or what he said is up for grabs right now), told him where his car was parked, they took him in for questioning (natural) and took his car (natural).
But the grounds for the search involved his lies and potential involvement in the murders...didn't they?
I think the grounds for JW's BMW search was because the 'ransom' cash was in his car earlier that day (this detail doesn't seem to be in dispute), which makes JW's car part of a crime scene.
But, I'd need to refresh my memory by reading the BMW SW.
ETA: Just realized I repeated FelicityLemon's original explanation "they would have done that anyway given that it was how the money was transported " - - so yes, I agree, LE would have searched JW's car anyway BECAUSE OF THE CASH being in the car. Nothing to do with any of his supposed lies or suspected involvement in the crimes.