Connecticut requires applicants to complete a safety course and have an NCIS background check. A Certificate of Eligibility is required for pistols, long guns, or ammunition. This certificate is valid for 5 years. There is a waiting period of 14 days for long guns. The waiting period does not apply to people who have a hunter's license or carry permit; also active duty military, and police.
Some states require that a citizen acquires a permit, before they purchase a gun. If it is required, there will be a fee that varies from state to state. Some states also require finger printing, and background checks before issuing the permit.