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While nothing he has done is illegal, in and of itself, the totality of all the messages could easily be construed as harrassment or stalking.
Most States allow you to get a restraining order against stalking and harassment, but Connecticut has no such provision.
However, harrassment is illegal. Here is the law in CT: http://crime.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=crime&cdn=newsissues&tm=7&gps=46_186_1295_862&f=00&tt=2&bt=0&bts=0&zu=http%3A//www.ncvc.org/src/main.aspx%3FdbID%3DDB_Connecticut195
in relevant part it reads: "...with intent to harass, annoy or alarm another person, he communicates with a person by telegraph or mail, by electronically transmitting a facsimile through connection with a telephone network, by computer network, as defined in section 53a-250, or by any other form of written communication, in a manner likely to cause annoyance or alarm; or (3) with intent to harass, annoy or alarm another person, he makes a telephone call, whether or not a conversation ensues, in a manner likely to cause annoyance or alarm."
So call the police.