I'd say that it depends on the situation. I deliver pizza for a living and they generally let me be. The general rule is that a pizza sign is like diplomatic immunity unless you are doing something really stupid. However, if I do get pulled over and have to deal with them I get real nervous and may lock up. I might also data dump at them unintentionally, depending on how the conversation goes.
I also have a sort of cop radar that lets me spot them fairly easily. I can tell the difference between a Crown Vic being used as a cop car and a civilian one simply by the way it is being driven (my detail oriented aspieness and automotive special interest don't hurt me here either!). Cops have a way of driving with a more commanding posture, if you will, with respect to normal traffic. It's hard to explain but it's just something you learn to pick out when you spend a lot of time on the road. I can also spot unmarked Chargers, Wimpalas and Tahoes this way too. (It doesn't hurt that the Tahoes are lowered and use a front air dam that makes their front ends distinctive!) I haven't seen one of the new Caprices yet, but those too will be easy to spot as they are not sold here as civilian vehicles (it's actually a Holden Kingswood from Australia, if memory serves.)
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Uncertain of diagnosis, either ADHD or Aspergers.
Aspie quiz: 143/200 AS, 81/200 NT; AQ 43; "eyes" 17/39, EQ/SQ 21/51 BAPQ: Autistic/BAP- You scored 92 aloof, 111 rigid and 103 pragmatic