Chiricahua National Park Act This bill redesignates the Chiricahua National Monument in Arizona as the Chiricahua National Park. The Department of the Interior shall ensure the protection of traditional cultural and religious sites in the park. Interior shall allow an enrolled member of any Indian tribe that is culturally affiliated with the land located within the boundaries of the park to collect plants, including parts or products of plants, and mineral resources within the park for noncommercial traditional, religious, customary, and cultural uses. Interior shall establish a tribal commission for the park in order to ensure that its management reflects the expertise and traditional and historical knowledge of members of applicable Indian tribes. The land located within the boundaries of the park is withdrawn from location, entry, and patent under the mining laws; and disposition under all laws pertaining to mineral and geothermal leasing. Any land or interest in land that is acquired by the United States for inclusion in the park shall be immediately withdrawn as specified above.