No. Connecticut DOES NOT recognize any other state's pistol permits. Nor does Connecticut have "reciprocity" with other states. However, Connecticut does offer non residents the ability to obtain a non resident Connecticut State Pistol Permit. Non residents can apply directly to the Connecticut State Police, Special Licensing and Firearms Unit.
You can obtain an application by calling 860-685-8494 to have an application mailed out, or by downloading one here: www.ct.gov/despp/lib/despp/slfu/pistol_permits/dps-799-c.pdf
More information on Connecticut's lack of "reciprocity" can be found in this Office of Legal Research document.