When is the apartment rush?

Sorry to ask what might be common knowledge, but when should we expect to see apartments come on the market in New Haven, particularly places like Westville and East Rock? Is there a particular website that would be good to check for listings? We are mostly interested in e.g. the bottom floor of 2 or 3 family homes. Ideally hoping to move to the area end of May or June, but listings seem sparse so far.

Thanks in advance.