I have been receiving calls from (207) 615-0342, 0343, and 0344 for a couple of weeks at least. They don't leave a message, and when I try to call any of those numbers back, I get a busy signal.

I have been getting calls from that number too! Did you ever figure out why they were calling?

I've been getting the same calls the past 2 weeks. The first time they called I picked up, expecting it to be related to business (however I'm from Rhode Island), they said they were calling on behalf of the state of Vermont's healthcare system to survey me to see how satisfied I am with RI's health care system - I told them I was driving in traffic and they simply said they will try again later. I blocked the call on my phone but they still keep calling with different numbers.

This sounds like a phishing scam to me. I would not recommend giving them any pieces of personal/identifiable information - do not confirm any date of birth, SSN, etc over the phone with them. A municipality of Vermont should not have a call coming from Portland, Maine.

It would be interesting if someone else got them on the phone (and in what region); I wonder if the story is the same or if it is different for each call.

Strange, I am also in RI and receive calls from this number and several others in the Portland Maine area. I'm curious if you have stayed at a Hilton hotel lately? Or shopped online at Puritans Pride or Amazon? These are the only companies I have given my number too in the last 2 months when these calls started.

I had a lot of missed calls from this number. So i answered one day and it was a survey about Health Insurance.