Securing death certificates may be done either through the mail or in person at the Town Clerk/Vital Statistics office in the down where the death occurred. 

Complete the Application for copy of Death Certificate available on the DPH website and mail it or bring it in person to the vital records office of the town or city where the death occurred. Certified copies are $20/each. Most town clerks do not accept personal checks.

See the Connecticut Town Clerk and Registrar Directory.  

Source: State of Connecticut, Department of Public Health