I am in the state of Utah and was just promoted to be a Customer Service Manager paid on salary. Am I entitled to overtime, or what other information is needed to determine that, or where can I go to find that out?

Assuming you are exempt, which you could be, there are no laws requiring you to be paid for working more than 40 hours a week.

Some of the more common exemptions under federal law can be found here

http://www.dol.gov/esa/regs/compliance/whd/fairpay/fact_exemption.htm

There are non-exempt folks who are salaried, but they get overtime. My bet is, that as a Manager, you may be exempt under the Executive Exemption (don't let the title fool you, supervisors and managers fall in that category and can qualify, if they have a salary of at least $455 a week and meet the tests for duties and responsibilities).