The 11 misdemeanors for which a permit must be revoked/denied are:
1. criminally negligent homicide (excluding deaths caused by motor vehicles) (CGS § 53a-58);
2. third-degree assault (CGS § 53a-61);
3. third-degree assault of a blind, elderly, pregnant, or mentally retarded person (CGS § 53a-61a);
4. second-degree threatening (CGS § 53a-62);
5. first-degree reckless endangerment (CGS § 53a-63);
6. second-degree unlawful restraint (CGS § 53a-96);
7. first-degree riot (CGS § 53a-175);
8. second-degree riot (CGS § 53a-176);
9. inciting to riot (CGS § 53a-178);
10. second-degree stalking (CGS § 53a-181d); and
11. first offense involving possession of (a) controlled or hallucinogenic substances (other than a narcotic substance or marijuana) or (b) less than four ounces of a cannabis-type substance (CGS § 21a-279(c)).
The other grounds on which the permit issuing authority must deny and revoke a permit are that the person:
1. is an illegal alien;
2. is under age 21;
3. failed to successfully complete a firearm safety and use course approved by the commissioner;
4. was discharged from custody in the preceding 20 years after a finding of not guilty of a crime by reason of mental disease or defect;
5. was confined by the probate court to a mental hospital in the 12 months before applying for a permit or certificate;
6. was convicted of a serious juvenile offense;
7. is subject to a firearm seizure order issued after notice and a hearing;
8. is prohibited under federal law from possessing or shipping firearms because he or she was adjudicated as a mental defective or committed to a mental institution (except in cases where the Treasury Department grants relief); and
9. is under a protective or restraining order for using or threatening to use force and in the case of possession, he or she knows about the order and if the order was issued in-state, he or she was notified and given a hearing opportunity (CGS §§ 29-28 and 29-32).
All of this doesn’t take into account the Lutenberg Amendment
Below from Wikipedia:
The Domestic Violence Offender Gun Ban often called “the Lautenberg Amendment” (“Gun Ban for Individuals Convicted of a Misdemeanor Crime of Domestic Violence”, Pub.L. 104–208, 18 U.S.C. § 922(g)(9)) is an amendment to the Omnibus Consolidated Appropriations Act of 1997 enacted by the 104th United States Congress in 1996, which bans access to firearms by people convicted of crimes of domestic violence. The act is often referred to as “the Lautenberg Amendment” after its sponsor, Senator Frank Lautenberg (D – NJ).
The act bans shipment, transport, ownership and use of guns or ammunition by individuals convicted of misdemeanor domestic violence, or who are under a restraining (protection) order for domestic abuse in all 50 states. The act also makes it unlawful to knowingly sell or give a firearm or ammunition to such persons.
The definition of ‘convicted’ can be found in the chapter 18 U.S.C. § 921(a)(33)(B)(ii) and has exceptions:
(i) A person shall not be considered to have been convicted of such an offense for purposes of this chapter, unless—
(I) the person was represented by counsel in the case, or knowingly and intelligently waived the right to counsel in the case; and
(II) in the case of a prosecution for an offense described in this paragraph for which a person was entitled to a jury trial in the jurisdiction in which the case was tried, either
(aa) the case was tried by a jury, or
(bb) the person knowingly and intelligently waived the right to have the case tried by a jury, by guilty plea or otherwise.
(ii) A person shall not be considered to have been convicted of such an offense for purposes of this chapter if the conviction has been expunged or set aside, or is an offense for which the person has been pardoned or has had civil rights restored (if the law of the applicable jurisdiction provides for the loss of civil rights under such an offense) unless the pardon, expungement, or restoration of civil rights expressly provides that the person may not ship, transport, possess, or receive firearms.
This law has been tested in federal court with the case United States v. Emerson (No. 99-10331) (5th Cir. 2001). See also U.S. v. Emerson, 231 Fed. Appx. 349 (5th Cir. 2007) (Same defendant seeking review of judgment). The case involved a challenge to the Constitutionality of 18 U.S.C. § 922(g)(8)(C)(ii), a federal statute that prohibited the transportation of firearms or ammunition in interstate commerce by persons subject to a court order that, by its explicit terms, prohibits the use of physical force against an intimate partner or child. Emerson does not address the portion of the Lautenberg Amendment involving conviction for misdemeanor domestic violence. It was initially overturned in 1999 for being unconstitutional, but that case was reversed upon appeal in 2001.
The case Gillespie v. City of Indianapolis, Indiana, 185 F.3d 693 (7th Cir. 1999) also challenged this law, and the case was rejected. The ex post facto aspects of the law were challenged with:
United States v. Brady, 26 F.3d 282 (2nd Cir.), cert. denied, 115 S.Ct. 246 (1994) (denying ex post facto challenge to a 922(g)(1) conviction) and
United States v. Waters, 23 F.3d 29 (2nd Cir. 1994) (ex post facto based challenge to a 922(g)(4) conviction).
Both of the challenges were denied.
Likewise this law was invoked in United States v. Jardee  where it was ruled that the threat of being subjected to the gun ban did not turn an otherwise “petty” crime into a “serious” one requiring a jury trial.
For more information and links to the above citation regarding the Lautenberg Amendment, click on the link below: