Is it a good idea to pet a K9 dog while it's investigating a crime?

Ok, I may or (may not) be myself right now so bare with me. This just popped up in my head.

Is it legal to even pet one while on the job?

So here's a scenario, the police are at an airport with a couple of dogs to investigate either a bomb or someone smuggling coke, one of the dogs sniff people walking past but this one guy who is teetering between balls of steel or just flat out stupidity and he's like "Wow what a cute dog" and petting his head and scratching behind the ears and all that.

My question is what would a police dog's reaction be? Would the guy or girl be in deep shit? Keep in mind these damn things are trained to mean business and could interpret any form of touching as an immediate threat. They're probably cute and lovable at the station but once they're scheduled for a job, it's a wrap.

EDIT: to clear things up. I don't mean like walking up to the dog while investigating. I mean like if a k9 (on a leash) was sniffing my legs and I decide to pet it not knowing it was an actual dog from the police force whos trained to kill me basically.