No Gun Tax Act of 1998

No Gun Tax Act of 1998 - Amends the Federal judicial code to prohibit a Federal officer, employee, or agent, including a State or local employee or officer acting on behalf of the United States (officer), from charging or collecting any fee in connection with a background check required in connection with the transfer of a firearm.

Amends the Federal criminal code to prohibit and set penalties for the unlawful retention, or transfer to another person, of firearms background check information by such officer or by a Federal contractor or consultant after: (1) the 24-hour period beginning with the receipt of such information on an individual who is determined not to be prohibited from receiving a firearm; and (2) the five-year period beginning with the receipt of such information on an individual who is prohibited from receiving a firearm.