Do you know who gave you the course? You might be able to get a copy of the cert from them...There is no time period within the statute.
You can always Call/Email DPS SFLU and ask. They are very friendly.
State of Connecticut
Department of Public Safety
Special Licensing and Firearms
1111 Country Club Road
Middletown, CT 06457
Telephone (860) 685-8290
[email protected]
http://www.cga.ct.gov/2009/pub/Chap529.htm#Sec29-28.htm
Sec. 29-28. Permit for sale at retail of pistol or revolver. Permit to carry pistol or revolver. Confidentiality of name and address of permit holder. Permits for out-of-state residents. (a) No person who sells ten or more pistols or revolvers in a calendar year or is a federally-licensed firearm dealer shall advertise, sell, deliver, or offer or expose for sale or delivery, or have in such person's possession with intent to sell or deliver, any pistol or revolver at retail without having a permit therefor issued as provided in this subsection. The chief of police or, where there is no chief of police, the warden of the borough or the first selectman of the town, as the case may be, may, upon the application of any person, issue a permit in such form as may be prescribed by the Commissioner of Public Safety for the sale at retail of pistols and revolvers within the jurisdiction of the authority issuing such permit. No permit for the sale at retail of any pistol or revolver shall be issued unless the applicant holds a valid eligibility certificate for a pistol or revolver issued pursuant to section 29-36f or a valid state permit to carry a pistol or revolver issued pursuant to subsection (b) of this section and the applicant submits documentation sufficient to establish that local zoning requirements have been met for the location where the sale is to take place except that any person selling or exchanging a pistol or revolver for the enhancement of a personal collection or for a hobby or who sells all or part of such person's personal collection of pistols or revolvers shall not be required to submit such documentation for the location where the sale or exchange is to take place.
(b) Upon the application of any person having a bona fide residence or place of business within the jurisdiction of any such authority, such chief of police, warden or selectman may issue a temporary state permit to such person to carry a pistol or revolver within the state, provided such authority shall find that such applicant intends to make no use of any pistol or revolver which such applicant may be permitted to carry under such permit other than a lawful use and that such person is a suitable person to receive such permit. No state or temporary state permit to carry a pistol or revolver shall be issued under this subsection if the applicant (1)
has failed to successfully complete a course approved by the Commissioner of Public Safety in the safety and use of pistols and revolvers including, but not limited to, a safety or training course in the use of pistols and revolvers available to the public offered by a law enforcement agency, a private or public educational institution or a firearms training school, utilizing instructors certified by the National Rifle Association or the Department of Environmental Protection and a safety or training course in the use of pistols or revolvers conducted by an instructor certified by the state or the National Rifle Association, (2) has been convicted of a felony or of a violation of subsection (c) of section 21a-279, section 53a-58, 53a-61, 53a-61a, 53a-62, 53a-63, 53a-96, 53a-175, 53a-176, 53a-178 or 53a-181d, (3) has been convicted as delinquent for the commission of a serious juvenile offense, as defined in section 46b-120, (4) has been discharged from custody within the preceding twenty years after having been found not guilty of a crime by reason of mental disease or defect pursuant to section 53a-13, (5) has been confined in a hospital for persons with psychiatric disabilities, as defined in section 17a-495, within the preceding twelve months by order of a probate court, (6) is subject to a restraining or protective order issued by a court in a case involving the use, attempted use or threatened use of physical force against another person, (7) is subject to a firearms seizure order issued pursuant to subsection (d) of section 29-38c after notice and hearing, (8) is prohibited from shipping, transporting, possessing or receiving a firearm pursuant to 18 USC 922(g)(4), (9) is an alien illegally or unlawfully in the United States, or (10) is less than twenty-one years of age. Nothing in this section shall require any person who holds a valid permit to carry a pistol or revolver on October 1, 1994, to participate in any additional training in the safety and use of pistols and revolvers. Upon issuance of a temporary state permit to the applicant, the local authority shall forward the original application to the commissioner. Not later than sixty days after receiving a temporary state permit, an applicant shall appear at a location designated by the commissioner to receive the state permit. Said commissioner may then issue, to any holder of any temporary state permit, a state permit to carry a pistol or revolver within the state. Upon issuance of the state permit, the commissioner shall make available to the permit holder a copy of the law regarding the permit holder's responsibility to report the loss or theft of a firearm and the penalties associated with the failure to comply with such law. Upon issuance of the state permit, the commissioner shall forward a record of such permit to the local authority issuing the temporary state permit. The commissioner shall retain records of all applications, whether approved or denied. The copy of the state permit delivered to the permittee shall be laminated and shall contain a full-face photograph of such permittee. A person holding a state permit issued pursuant to this subsection shall notify the issuing authority within two business days of any change of such person's address. The notification shall include the old address and the new address of such person.