Local Government Internet Tobacco Sales Enforcement Act of 2004 - Amends the Jenkins Act to require each person who engages in an interstate sale of cigarettes or smokeless tobacco or in an interstate distribution of cigarettes or smokeless tobacco to comply with all applicable excise, sales, and use tax laws in the State and place in which the cigarettes or smokeless tobacco are delivered.
Prohibits the cigarettes or smokeless tobacco from being delivered to the buyer unless in advance of the delivery the excise tax has been paid and any required stamps or other indicia that such tax has been paid are properly affixed or applied, with an exception.
Authorizes a State attorney general or the chief law enforcement officer of a local government that imposes an excise tax on cigarettes or smokeless tobacco to bring a civil action to obtain appropriate relief against anyone who violates such prohibition or who knowingly assists or participates in such a violation.
Declares that the Act does not prohibit an authorized State, local, or tribal government official from proceeding in State or tribal court.
Makes the Act's provisions regarding State tax collection inapplicable to certain sales that occur exclusively in Indian country.
Expresses the sense of Congress that unique harms are associated with the remote interstate sales of cigarette and smokeless tobacco. Affirms Congress' longstanding interest in encouraging compliance and enforcement of State laws that relate to remote (including Internet) sales of such products.