The closest train station to the property you referenced on Hope St. would be the Glenbrook neighborhood train station in Stamford. It's located off of Church St. and Glenbrook Rd.
The main station is situated downtown off Washington Blvd. near I95 between exits 7 and 8. There is also a station in the Springdale area on Hope St. near Largo Drive.
Here is the link to Metro North's schedule which includes the New Haven line: