The officer should give you a summary report which only includes the names and vehicles of the parties involved (and nothing else). The officer should have given it to you on site or brought it to you if you were transported to the ER. If you want the full report, you have to ask for it here for a fee. Usually insurance will get it for themselves. If you have nothing to contest it’s a bit of a waste of money to get it.

Edit: forgot to mention the summary includes the case number of the full crash report. So yeah, maybe try calling the nearest station of the police/trooper that was on site to get this number.