Light aircraft pilot reported an NMAC with a helicopter in the vicinity of the Statue of Liberty.

Narrative

I was circling the Statue of Liberty. I was complying with all NYC SFRA procedures (ie circling at the required altitude and circling counter clockwise). After making my call on the CTAF frequency; I initiated my turn. About halfway round a helicopter came up from behind me and started heading straight for my aircraft. I took evasive action to avoid a collision but as he was behind me I could not see him until he got within 40 ft. of my aircraft. I immediately climbed and I entered the NYC Class Bravo airspace. As soon as the conflict cleared I descended to a safe level (about 5-10 seconds later). While I regret violating the airspace; it was the only way to avoid a collision. I have flown the NYC SFRA on multiple occasions and there are an abundance of helicopters that do not talk on the CTAF frequency as required. In fact; most of the conversation on that frequency is jovial and not related to aviation. I feel there should be strict rules to ensure radio compliance of aircraft flying in the SFRA and a system set in place to keep apart transient aircraft and local helicopter operations