National Health Museum Site Selection Act

Requires the Museum to provide written notification to the Administrator of the date on which it will accept conveyance of the property.

Sets forth provisions regarding the purchase price for the property, including requiring the Administrator to report the purchase price to Congress and to deposit it into the Federal Buildings Fund.

Provides for reversion of the property to the United States and repayment of the purchase price to the Museum if : (1) it is used for a purpose other than construction and operation of the Museum; (2) the Museum does not commence construction on the property within three years after conveyance, other than for a reason not within the Museum's control; or (3) the Museum ceases to be a nonprofit corporation.

Permits the Museum to: (1) demolish or renovate any existing or future improvement on the property; (2) build, own, operate, and maintain new improvements on the property; (3) finance and mortgage the property on customary terms and conditions; and (4) manage the property.

Requires the United States to cooperate with the Museum on any zoning or other matter relating to the development or improvement of the property or the demolition of any improvement.

Requires the costs of remediation of any environmental hazards existing on the property, including all asbestos-containing materials, to be borne by the United States.

Requires the Museum to submit annual reports to the Administrator and Congress on the status of planning, development, and construction of the Museum.