the first few miles of the trail from the Banton St. starting point which is at the Mobil Station off the parkway in North Haven run along the Quinnipiac River can be wet and swampy and at times of flooding or heavy rains are impassable , Last time out was overgrown in areas and in need of trail work both brush clearing and trail marking. Then a short road walk ( about 1/2 mile) and back on the trail that takes you over and through sleeping giant state park which is nice hiking and all of those trails have recently been cleared and reblazed ; crew was out finishing up this past weekend when I was there.
Many trails through sleeping giant to choose from , blue probably has the most to offer ( past castle and over the head has best views), you can download a trail map from the sleeping giant web sight. Hope this helps.