American Apprenticeship Act This bill directs the Department of Labor to make grants to assist states to pay for the cost of carrying out projects that defray the cost of instruction associated with pre-apprenticeship and apprenticeship programs, as those terms are defined by this bill. A state must use grant funds to defray the costs of tuition and fees, textbooks, equipment, curriculum development, and other required educational materials. Labor shall: (1) identify in-demand occupations that lack the use of apprenticeships, (2) analyze the use of the apprenticeship model in those occupations, and (3) report on such analysis to states and Congress.