Poor Kanako is so stressed but, more importantly, lonely. And he's...not a great cop, all things considered.
I agree that cop dude is kind of being unpleasant.
I'm sure he's a good guy, but also, he's unintentionally being a creep. She's pretty clearly uncomfortable around him and most of the relationship progress he's made with her has been from a severe position of power-though only some of it would apply if she wasn't the culprit he was looking for.
It's like asking out someone working in the service industry-they're paid to be nice to you and can't leave, so it's poor form.