State Grazing Management Authority Act This bill requires the Bureau of Land Management (BLM) and the Forest Service, upon the request of a state, to enter into cooperative agreements providing for the state to manage grazing allotments on eligible federal land in that state. Land is eligible if it is subject to a grazing permit or lease issued by the BLM or the Forest Service and has periodically or historically been used or offered for livestock grazing. At the request of a state, a cooperative agreement shall include an assignment to the state of the environmental review responsibilities of the BLM or the Forest Service under the National Environmental Policy Act of 1969 (NEPA) with respect to an allotment management plan. A cooperative agreement shall include, with respect to an allotment management plan, the assignment to a state of the responsibilities of the BLM or the Forest Service to approve or construct water infrastructure improvements to improve public grazing. A state that enters into a cooperative agreement shall establish a commission to advise the state on the substance and terms of the agreement and any matters related to carrying it out. A cooperative agreement shall provide for the development of a process by a state to resolve disputes related to a decision by the state with respect to an allotment management plan.