Wow, I appear to be first for this number! I suspect a long list of call complaints will follow.
For some reason, this number is vaguely familiar to me, but nothing turns up on a google search. I think it's because I get a lot of spam calls from that area code and the first three numbers, with different last-four-numbers. Same company of scammers and spammers.
It's definitely one of those caller banks where the computer dials a lot of numbers at once and you say "hello" a few times before an actual human talks to you. I could hear people talking in the distance, as if it were a telemarketing bank of callers. I said hello three times, nobody answered, then I hung up.
I called 203-763-1967 back and instantly got a female pre-recorded voice telling me to press "1" to be added to their do not call list. I did not want to alert them to the fact that my phone number is live, so I just hung up without pressing "1". I note that another 203-763-xxxx numbers mentioned on 800notes.com bill you if you press a number on their prompt during a call, so that warned me off pressing the number "1", too. I didn't want a charge to show up on my phone bill next month.