If the inmate in question is a guest of the state, then nearly every state's department of corrections website has a way to search inmates, and their release dates are usually included in this information. This information is generally updated regularly, so it's usually reliable.
If the inmate is in a city or county jail, a call to the warden's office will usually produce the information. Release dates are public record, just like arrest records, so anyone should be able to get this information just for the asking. If not, it's probably time to call the media and enlist its assistance in finding out what's going on.