This is an ongoing scam which appears to originate in Puerto Rico or the Dominican Republic. It seems to be striking the northeast section of the US. I would definitely go to the police and make a report. They may not immediately be able to find the people making the calls but they can go to the media and let people in the local community know what's happening and that people should be on the lookout for this scam. Yes, by all means make a police report. But, go in person. Don't try to phone it it in, because the person on the line will simply say something to the effect that it's a scam and just forget about it. You need a paper report. And your local LE needs to go to the media. They will, if enough people complaint.
This also happened to my husband. Thank goodness my husband knew this was a scam because the person on the other end who claimed to be an EMT said that the girl who was bleeding and unconscious listed my husband as an emergency contact. My husband then asked this gentleman her name but he could not identify her. My husband felt that if this man could find him he could of found his patient's name. Oldest scam around.