AFAIK CT has a two week long gun waiting period unless you have a CCW license. I don't think a NYS Pistol or hunting license is acceptable but it might be. I would call a CT dealer in advance to verify if there are any exceptions for a NY resident. If you need a NY FFL let us know what county you are in.
www.cga.ct.gov/2005/pub/Chap529.htm#Sec29-37a.htm Sec. 29-37a. Sale or delivery at retail of firearm other than pistol or revolver. Procedure. (a) No person, firm or corporation may deliver, at retail, any firearm, as defined in section 53a-3, other than a pistol or revolver, to any person unless such person makes application on a form prescribed and furnished by the Commissioner of Public Safety, which shall be attached by the vendor to the federal sale or transfer document and filed and retained by the vendor for at least twenty years or until such vendor goes out of business. Such application shall be available for inspection during normal business hours by law enforcement officials.
No sale or delivery of any firearm shall be made until the expiration of two weeks from the date of the application, and until the person, firm or corporation making such sale, delivery or transfer has insured that such application has been completed properly and has obtained an authorization number from the Commissioner of Public Safety for such sale, delivery or transfer. The Department of Public Safety shall make every effort, including performing the national instant criminal background check, to determine if the applicant is eligible to receive such firearm. If it is determined that the applicant is ineligible to receive such firearm, the Commissioner of Public Safety shall immediately notify the person, firm or corporation to whom such application was made and no such firearm shall be sold or delivered to such applicant by such person, firm or corporation. When any firearm is delivered in connection with the sale or purchase, such firearm shall be enclosed in a package, the paper or wrapping of which shall be securely fastened, and no such firearm when delivered on any sale or purchase shall be loaded or contain any gunpowder or other explosive or any bullet, ball or shell.
(b) Upon the delivery of the firearm, the purchaser shall sign in triplicate a receipt for such firearm which shall contain the name and address of such purchaser, the date of sale, caliber, make, model and manufacturer's number and a general description thereof. Not later than twenty-four hours after such delivery, the vendor shall send by first class mail or electronically transfer one receipt to the Commissioner of Public Safety and one receipt to the chief of police or, where there is no chief of police, the warden of the borough or the first selectman, of the town in which the purchaser resides, and shall retain one receipt, together with the original application, for at least five years.
The waiting period specified in subsection (a) of this section during which delivery may not be made and the provisions of this subsection shall not apply to any federal marshal, parole officer or peace officer, or to the delivery at retail of (1) any firearm to a holder of a valid state permit to carry a pistol or revolver issued under the provisions of section 29-28 or a valid eligibility certificate issued under the provisions of section 29-36f, (2) any firearm to an active member of the armed forces of the United States or of any reserve component thereof, (3) any firearm to a holder of a valid hunting license issued pursuant to chapter 490, or (4) antique firearms. For the purposes of this section, "antique firearm" means any firearm which was manufactured in or before 1898 and any replica of such firearm provided such replica is not designed or redesigned for using rimfire or conventional centerfire fixed ammunition except rimfire or conventional centerfire fixed ammunition which is no longer manufactured in the United States and not readily available in the ordinary channel of commercial trade.