You need a liberation permit:

Importation and/or Liberation Permit (General) - Word Form / PDF
Authorizes the importation of live fish or live fish eggs from out-of-state and/or the liberation (stocking) of live fish or live fish eggs into Connecticut waters. A liberation permit is necessary whenever an individual or organization stocks live fish or fish eggs into any pond, lake or stream in Connecticut. An importation permit is required for the importation into Connecticut of live fish or fish eggs.

And, a private waters permit:

Private Waters Designation
The registration of private waters is required for any owner of private waters who desires to remove fish from such waters.

Towards the bottom of this page:
http://www.ct.gov/deep/cwp/view.asp?a=2696&q=322716&deepNav_GID=1630