Regardless of whether you classify it as a disease, the CDC does in fact track and research car accident deaths and injuries: https://www.cdc.gov/vitalsigns/motor-vehicle-safety/index.ht...

Additionally there are two federal agencies (NHTSB and NTSB) that regulate the various elements of vehicular safety at the national level, on top of state DMVs and transportation departments. By comparison, the federal BATFE is basically hamstrung on firearms regulation, and outside a few States so are its state level equivalents.