The phrase "connection with the accident" means having some kind of relationship or involvement with the accident. It indicates a link or association between someone or something and the event happening. Full definition
It is a good idea to get pictures of the vehicles involved in the accident if you can, as the police may not take pictures in connection with the accident report. (renopersonalinjurylawyer.com)
In such cases, the plaintiff alleges that the defendant acted in a negligent or careless manner in connection with an accident or injury that caused harm. (schiffrinpa.com)
These include agencies that employ motor vehicle operators, FAA for airman medical certifications, FRA (and railroads) for locomotive operators, Coast Guard for merchant mariners and servicemen, and NTSB and FMCSA in connection with accident investigations. (transportation.gov)