Make the people in the crowd feel as though they are the smart ones and that you merely want to learn from them. Then go on about your business. In case I can't make something out, give me a phone number where I can reach you if I have any questions. With the statement in their handwriting, it can be concluded later that the statement is indeed theirs. That can come back to haunt you months later.
Some witnesses try to be too helpful.
They will tell you what they think they saw, not what actually happened. Just ask them what they saw. After you have accumulated the statements, made all your measurements, taken photographs, and filled in the blanks on your crash report, you get the scene cleared and go back on patrol or head off on another assignment. Maybe there is still a lot more investigating to be done, or perhaps you need to do some reconstruction. This involves vehicle damage analyses, preparing scale diagrams, mathematical computations, and so on.