I just check the GPS HazMat route and the National HazMat Route Registry. I wish the NHRR was easier to decode on a smartphone. Also try Googling hazmat route and state. The NY Port Authority has a concise online handbook covering what HM is allowed/prohibited on the Port Authority bridges and tunnels.
Don't forget several states require all HazMat loads to enter open weigh stations despite what your electronic doo-dad says about bypass. I think the AZ fine for bypassing the scale with a HM load is $600.