Like Paul D posted (Thanks Paul!), on private land you can use pretty much anything you want outside of deer season. State land is where you start getting into caliber restrictions...basically .22 or .17 rimfires and shotguns with shot larger/heavier than #2. And if you want to go all Jeremiah Johnson on us, you can use a muzzleloader for small game on state land as long as it is no larger than .36 caliber and you can only use a single projectile.

Here's the applicable sections of the regulations for your reading pleasure:

HUNTING AND TRAPPING
26-66-1. Behavior and actions of hunters

(a) The method of taking wild birds and wild quadrupeds by hunting shall be restricted to firearms, high velocity air guns using a single ball or pellet type projectile, and compound, long, or recurved bow. In designated areas, by special permit, the commissioner may allow the use of modified versions of air guns or archery implements to achieve wildlife management objectives. No arrow or projectile which is coated with or contains any drugs, poison or known tranquilizing substance may be used or possessed while engaged in archery hunting.

(b) Use of crossbows is prohibited, except that a person who has a permanent physical disability to the degree that he or she cannot operate a long, recurve or compound bow may obtain a permit to take deer or turkey with a crossbow. A person applying for this permit must show proof that he or she has successfully completed the Connecticut conservation education/firearms safety advanced bowhunter education course or its equivalent, and must personally appear before the commissioner, or his designee, with certification from a licensed physician that he or she is so disabled. Upon satisfactory proof of disability, the commissioner may issue such a permit under this section which must be carried at all times while hunting. Such permit shall not be a replacement for and is valid only with any license or permit required for archery hunting under the provisions of chapter 490 of the Connecticut General Statutes or regulations promulgated thereunder. Any crossbow and bolt combination to be used for hunting as permitted under this subsection shall meet the following specifications: (1) The draw weight of the crossbow shall be not less than 125 pounds nor more than 200 pounds; (2) The crossbow shall have a permanent fixed rifle type stock, and a functional and/or fully operational mechanical safety device; (3) The bolt (arrow) length shall be not less than eighteen inches, excluding the broadhead; (4) The bolt weight shall be not less than 450 grains, including the broadhead; (5) the broad head shall have two or more blades with a width not less than seven-eighths of an inch at the widest point. In addition, any crossbow in a drawn and cocked position shall be considered a loaded weapon, whether or not a bolt is loaded on the crossbow.

(q) Rifles and handguns using centerfire ammunition or rim fire ammunition having a cartridge case longer than that of a.22 rim fire long rifle cartridge case and projectile of which is heavier than 20 grains and shotgun ammunition of loads larger or heavier than number two shot shall not be possessed and pistols or revolvers using ammunition larger or heavier than .22 rim fire long rifle cartridge shall not be used for the purposes of hunting as defined in section 26-1 of the Connecticut General Statutes on any private land during the private land shotgun/rifle deer season as specified in section 26-86a-6(d) of the Regulations of Connecticut State Agencies. This provision relating to rifle and shotgun ammunition shall not apply to persons holding valid private land shotgun and/or rifle deer permits. Waterfowlers hunting from a boat, blind or stationary position may only use the ammunition specified in section 26-66-4(t) of the Regulations of Connecticut State Agencies.

(r) No person shall hunt, pursue, wound or kill any wildlife from September 1 through the last day of February without wearing above the waist at least a total of four hundred square inches of fluorescent orange clothing visible from all sides. This provision does not apply to: (1) archery deer hunting during the open season for hunting deer with bow and arrow; (2) archery deer hunting during the private land muzzleloader or shotgun/rifle deer seasons while hunting from an elevated tree stand more than 10 feet from the ground in zones designated by the commissioner; (3) archery and firearms turkey hunting; (4) waterfowl hunting from blinds or boats or from a stationary position; (5) crow hunting from a blind or a stationary position; (6) hunting raccoon and opossum from one-half hour after sunset to one-half hour before sunrise; or (7) deer hunting by a landowner on his own property.

26-66-2. State-owned, state-leased and permit-required hunting areas; weapons
(a) Any rifle or handgun using centerfire ammunition may not be used to hunt on state-owned land. Any rifle or handgun that uses rim fire ammuntion having a cartridge case longer than that of a .22 long rifle catridge case and the projectile of which is heavier than 20 grains, muzzleloading rifles larger than .36 caliber or using any projectile other than round ball, crossbows and shotgun ammunition of loads larger or heavier than number two shot shall not be possessed or used for the purposes of hunting as defined in section 26-1 of the Connecticut General Statutes on any state-owned land, including state forests. This provision shall not apply to rifles possessed by persons transporting legally killed and properly tagged deer taken on private lands to check stations located on state-owned properties, approved rifle range areas or deer hunting wi