Say you are a new author and the book you are writing has a character in it that resembles a TV character--not in physical appearance, but in speech. They are both very smart and have an arrogant and snobby personality. How do I know where the cutoff lies in infringing on this TV character's copyright laws?
What is the name of your state, larryh, or if not in the US, what is the name of your country?
The odds are pretty good the character is not protected under copyright laws. Very few TV characters are original and creative enough to qualify for copyright protection. There could be a trademark on a character, however, and that might be a bigger risk.
A snobby personality and arrogance in a character would not be characteristics that are likely to cause a legal issue on their own. A lot of people are arrogant and snobby. A bigger concern would be if you patterned your character after a real life person who can be recognized through the character's description or by context.
That said, you probably do not want your character to be a Sheldon clone (from "Big Bang Theory") or a duplicate of ... actually I can't offhand think of another truly original TV character.
You can have a publishing law professional check out your character for a problematic resemblance, though, if you have concern that your character too closely resembles another author's character.