Limiting Inhumane Federal Trapping Act This bill prohibits any personnel of the Department of the Interior or the Department of Agriculture (USDA), in performing their duties, from using, recommending, training in the use of, or planning for the use of, any body-gripping trap used to kill or capture an animal. This prohibition does not apply to training in the dismantling of body-gripping traps that have been illegally placed. No person shall use or possess any body-gripping trap on property under the administrative jurisdiction of Interior or USDA, except in Indian country, regardless of whether the person is employed by, or is working under a contract with, Interior or USDA. Such prohibitions shall not apply to the use of a body-gripping trap to: control documented, invasive species to achieve resource management objectives where alternative methods have failed; or protect a species that is listed as an endangered or threatened species or treated by the Forest Service as a sensitive species. Such exceptions shall not apply unless: such use of a body-gripping trap is in accordance with state and federal law; prior to using such a trap, all available and viable nonlethal methods for such control or protection have been attempted; and such attempts have been documented in writing, and the documentation is maintained at the headquarters of the department that employs the individual engaging in such attempt. The bill imposes criminal penalties for violating the prohibitions in this bill.