It has a similar meaning (it's not very common in British English, but I have heard it used) - if someone gives you the third degree, they fiercely and harshly interrogate you to get something out of you. Whether you confess or not is irrelevant, if my dad 'gave me the third degree' he questioned me at length to establish something.

Some countries/states categorize crimes into "degrees". First degree murder is the worst kind of murder. Second and third degree are less severe kinds of murder. Maybe that person didn't have the intent to kill, only to harm, but the victim died anyway.

Jon's answers is correct. There's nothing else we can add now really, except I will just add that being given the third degree does not always have to mean 'fiercely and harshly interrogate', we can also use it in more causal ways, where a better way to describe it I think would be 'persistently question' like just if a friend is asking you a lot of questions about something, they might not be being harsh like a police officer etc, just asking and asking again and again, lots of different questions, then we might say something like what is this, you're given me the 3'rd degree now? Stop giving me the 3'rd degree.