No close encounters of the police kind in this Z (yet) - but I got pulled over two different times in my old 300ZX TT back in the 90's "just to make sure I actually owned it"
Once I pulled myself over... Same 300ZX TT, also back in the 90's: I was goofing off with some Porsche at like 2am on highway 36 between Boulder and Denver, at ludicrous speed, when I noticed rollers WAAAAAAY back there - like a couple of miles back there...
The Porsche took off and I pulled over to wait for the hammer... The officer had no idea how fast I was actually going, but knew it was too damn fast - but being as I was at least pretending to be a responsible adult he let me off with a warning.