Connecting America's Active Transportation System Act This bill directs the Department of Transportation (DOT) to carry out an active transportation infrastructure investment program to provide competitive grants for states, Indian tribes, multi-county special districts, and local or regional government organizations to construct certain projects to provide safe and connected active transportation facilities, including for sidewalks, bikeways, and trails that connect between destinations within a community or between communities, metropolitan regions, or states. DOT must select grant recipients within 150 days after funds become available under this bill. The bill sets forth various limitations on the use of funds, including that DOT must obligate at least 30% of funds to certain projects, including projects that connect people with public transportation, businesses, workplaces, schools, residences, recreation areas, and other community activity centers; set aside at least $3 million to provide planning grants for eligible organizations to develop plans for active transportation networks and active transportation spines; and set aside at least $2 million to cover the costs of administration, research, technical assistance, communications, and training activities under the program. The federal share of grants must not exceed 80% of the total project cost.