Anti-Gun Trafficking Act of 1995 - Amends the Federal criminal code to prohibit any licensed firearms importer, manufacturer, or dealer from transferring: (1) two or more handguns to an unlicensed individual during any 30-day period; or (2) a handgun to an unlicensed individual who received a handgun during the 30-day period ending on the date of the transfer.

Bars any unlicensed individual from receiving two or more handguns during any 30-day period.

Prohibits any licensed importer, manufacturer, or dealer from transferring a handgun to an unlicensed individual unless the seller has: (1) received from the individual a statement containing specified information, including the individual's name, address, and date of birth appearing on a valid identification document containing a photograph and a statement that the individual is not a fugitive; (2) verified the individual's identification by examining the identification document; and (3) within one day after the individual furnishes the statement, provided a copy of the statement to the chief law enforcement officer of the individual's place of residence.

Makes such provisions inapplicable to the transfer of a handgun to, or the receipt of a handgun by, an individual who has presented to the seller a written statement, issued by the chief law enforcement officer during the ten-day period ending on the date of the transfer or receipt, that the individual requires access to a handgun because of a threat to the life of such individual or of any member of such individual's household.

Requires any seller of a handgun who, after the transfer, receives a report from a chief law enforcement officer that receipt or possession of the handgun by the transferee violates Federal, State, or local law to immediately communicate all information the seller has about the transfer and the buyer to the chief law enforcement officers of the place of business of the seller and of the place of residence of the buyer.

Sets forth provisions regarding: (1) confidentiality of information; (2) recordkeeping; and (3) penalties for violation of this Act.