This is the actual statute.
Sec. 53-341b. Sale or delivery of body armor restricted. (a) No person, firm or corporation shall sell or deliver body armor to another person unless the transferee meets in person with the transferor to accomplish the sale or delivery.
It basically is just an attempt to force manufacturers not to ship to individuals. Only to Gov agencies.
Since people convicted of certain felonies can not possess body armor in CT.
Sec. 53a-217d. Criminal possession of body armor: Class A misdemeanor. (a) A person is guilty of criminal possession of body armor when he possesses body armor and has been (1) convicted of a capital felony, a class A felony, except a conviction under section 53a-196a, a class B felony, except a conviction under section 53a-86, 53a-122 or 53a-196b, a class C felony, except a conviction under section 53a-87, 53a-152 or 53a-153 or a class D felony under sections 53a-60 to 53a-60c, inclusive, 53a-72a, 53a-72b, 53a-95, 53a-103, 53a-103a, 53a-114, 53a-136 or 53a-216, or (2) convicted as delinquent for the commission of a serious juvenile offense, as defined in section 46b-120.
I am not aware of any requirement for the seller in a face to face sale to run a background check though.