Handgun Registration Act of 2001 - Amends the Omnibus Crime Control and Safe Streets Act of 1968 to provide for an increase by 15 percent of drug control and system improvement (Byrne) grant funds available to a State that has in effect a law which requires: (1) each individual to whom a handgun is transferred to complete a handgun registration form that includes specified information identifying the transferee, the handgun, and the transferor and proof of insurance coverage for the transferee's liability to any person who, while engaged in lawful activity, suffers bodily injury or death through the misuse of that handgun resulting from the transferee's negligence; (2) each individual who possesses a handgun to complete a handgun registration form that includes information identifying the individual and the handgun; and (3) the chief law enforcement officer of the State to furnish information from handgun registration forms to Federal, State, and local law enforcement authorities upon request.