Anti-Gunrunning Act of 1999

Provides for imprisonment for up to five years (currently, one year) for a licensed dealer, importer, manufacturer, or collector who knowingly makes any false statement in connection with required firearms records.

Extends the deadline for the destruction of records relating to handgun transfers subject to the waiting period from 20 business days to 35 calendar days after the date the transferee made the statement on the basis of which notice of the transaction was provided to the chief law enforcement officer of the place of residence of the transferee. Requires the national instant criminal background check system, if receipt of a firearm would not violate Federal or State law, to destroy records relating to the person or the transfer within 35 calendar days after the date the system provides the licensee with the identification number unique to the transfer.