CT DEP hunting guide specifically states .22 and .17 rimefire are legal on state land.
http://www.ct.gov/dep/cwp/view.asp?a=2700&q=491352&depNav_GID=1633
Rifles and Handguns: Rifl es or handguns using
ammunition larger or heavier than .22 caliber
rimfi re long rifl e cartridges are prohibited on
state-owned land. Rifl es or handguns of any
caliber are prohibited on State-leased and Permit-
Required Hunting Areas (see Permit-Required
and State-Leased Hunting Area sections for
exceptions). The use of rifl es or handguns to
hunt turkeys, waterfowl, or any other federally
regulated migratory game bird (except crows)
is prohibited. Hunting on private land with
ammunition larger than .22 caliber rimfi re long
rifl e during the private land shotgun/rifl e deer
season is prohibited unless the user has a valid
private land deer season permit and landowner
consent form. The use of rifl es or revolvers to
hunt deer is subject to additional restrictions
(see Private Land Shotgun/Rifl e Season). The use
of ammunition larger or heavier than .22 caliber
rimfi re long rifl e to hunt raccoon or opossum at
night is prohibited. A person using a handgun
for hunting must possess any required state/
town permits to carry. Note that it is legal to
use .17 caliber rimfi re fi rearms in all situations
where it is legal to use .22 caliber rimfi re long
rifl e fi rearms.