I thought the prosecutor asked the sheriff to do that, not Vinny.
But the scene only works because Mona Lisa is mad at Vinny, has no idea what he’s doing, and it finally dawns on her that he figured out the solution to win the case.
I listened to the director Jonathan Lynn’s commentary on the movie and recommend it: it’s way more interesting than most movie commentaries (especially by directors).
Per the commentary: Lynn wasn’t happy about how precisely that scene identified the murderer’s vehicle either. What he wanted was just enough to prove conclusively that there’s no way “the two yutes” car could have made those tire tracks and thus get them acquitted; however, the studio wanted a resolution to the case. He went along with them because they were the money, of course, but by his own definition it was too deus ex machina.
The other thing he wanted to include was a scene of [Ralph Macchio’s character’s] mother having a heart attack to explain why she was absent, but the studio nixed it due to time and expense. Lynn felt people would wonder why this close knit Italian family didn’t come to the trial, but said that in fact not one person ever questioned it.
No, it was definitely Vinny who asked the sheriff to do that. As I remember, he first refused, saying (more or less), " It’s not my job. You do your own investigating."
And she finally gets to say that he’s wrong about something.
For example: In Legally blond “Every cosmo girl knows you can’t wet your hair for 48 hours after a perm” Factually incorrect. You can wet it all you want. You can’t shampoo your hair for 48 hours after.However,even if you shampoo it you probably will be okay.