[VRWC_minion]

Absent an express statement by Congress on a particular issue, a state's power to assert its civil regulatory laws . . . on a federal reservation, turns on whether state law in that area is preempted by the operation of federal law. New Mexico v. Mescalero Apache Tribe, 462 U.S. 324, 103 S.Ct. 2378, 2386 (1983).

I would assume that federal law is silent on smoking bans.

[VRWC_minion]

On a related issue

In determining whether a state regulatory law applies to a tribe on a federal Indian reservation, the courts apply a two part test to determine if state law has been preempted: (1) whether application of state law would "interfere with reservation self-government," which inquiry is informed by traditional and historical notions of tribal sovereignty; and (2) whether application of state law "would impair a right granted or reserved by federal law." Rice v. Rehner, 463 U.S. 713, 103 S.Ct. 3291 (1983). In Rice v. Rehner, the United States Supreme Court expressly determined that: "tradition simply has not recognized a sovereign immunity or inherent authority in favor of liquor regulations by Indians." Id., 103 S.Ct. at 3297. The Supreme Court found that: "The State has an unquestionable interest in the liquor traffic that occurs within its borders, and this interest is independent of the authority conferred on the States by the Twenty-First Amendment." Id., at 3298.