[DannyBee]

"No it doesn't"

This is true but not for the reason you cite. It would be stalking if they make a statement that will place the person in reasonable fear of harm. If they did that, in most states, it won't matter whether they are doing it as cops or not. Some states have "no lawful justification" in the text (which would protect police), but most don't.

Various states do have laws that would cover this that are not stalking (violations of various invasion of privacy, wiretapping, etc).

Most are written in the way that it will be unlawful even if they are police.