They also say victims are sometimes told that they must provide bank account or credit card numbers and other information in order to claim their "winnings."
In some cases, victims have been sent checks that are supposed to cover the taxes and fees, but after they attempted to cash them, they found out the checks were fake.
Fraud investigators have received several reports about the scam in recent months.
Potential victims have been notified of the bogus lottery or sweepstakes "winnings" through telephone calls and mail.
According to investigators, in one case an elderly person was conned out of more than $50,000.
Authorities warn if someone tells you that you've won a sweepstakes, be skeptical, never give out personal information and never agree to wire money in order to claim a prize.
The Durham Police Department is currently investigating the case.