American Apprenticeship Act This bill directs the Department of Labor to make grants to assist states in carrying out projects that defray the cost of instruction associated with pre-apprenticeship and qualified apprenticeship programs. Labor shall (1) establish performance measures and an evaluation system for such grant program; and (2) identify in-demand occupations that lack the use of apprenticeships, analyze the use of the qualified apprenticeship program model in those occupations, and report on such analysis to states and Congress.