Sure, there are limits. But the limits vary from person to person, depending on how gullible the listener is.
The rule of thumb? Unless the patrolman in question is under oath, the cops can lie about anything at any time to anyone. Sure there are exceptions, such as “Am I under arrest? Am I being detained? Am I free to go?”, which must be answered truthfully but the listener’s gullibility has nothing to do with the limits a cop can push. No matter if I am the sage of the ages or a common fool, a cop can lie to me, to my face, about darned near anything at any time. They are not at all obligated to answer truthfully if one is under investigation; indeed there are situations where prudence would command they lie about that. How do you think “going undercover” works?
The only time cops are involved in a situation is when someone is going to jail, and there has never once been a case when they’ve been “picky” about who they take. Even if you yourself were the one who called them, only a fool would let a cop into their house (they are to be considered as dangerous animals, on par with tigers and such), and only a fool would speak unguarded around one. Never in the history of arrests has anyone ever “talked” their way out of being arrested by being “clever”. A cop’s “bullshit detector” is no more reliable than yours or mine, but the difference is even when their’s falsely detects a positive they can lock someone up in handcuffs and haul them off, so never try to “trick” or “talk around” a cop. Like Joe Friday says, keep it to just the facts ma’am and rest assured “I don’t want to answer that” is both truthful and factual.
And never, ever, even think about touching a cop. I don’t even shake their hand.