The true summit of County House Mountain lies on private property, though the summit ridge is part of the Pequest Wildlife Management Area.
Parked at N 40 48.769 W 074 58.265, and from here you can take the woods road and bear left at the two splits, which will take you relatively close to the summit. In our case, we did Oxford first, and then straight-line whacked to CH before taking the woods road back out. We got about 250' from the summit before turning away at the posted signs, as it's not quite like failing that close to the top of Everest. If you do this solo, it would be supremely easy, but combining it with Oxford and the subsequent whack it was a bit nasty with tons of rocks and stickers.
Followed suggestion of Brom and parked on Axford Ave on an NJ WMA parking area. Followed a narrow pathway/woods road for a while which eventually petered out. Kept in a SE direction, crossed a paved driveway and could see a house to my left. Found another better woods road and followed that for a while until it became clear I need to hang a left and bushwhack in the direction of County House Mountain. The going was relatively smooth and open and got steeper closer to the summit. Summit area was very clearly posted with multiple signs. I did not pass those signs but got as close as I could and then turned my thoughts toward Oxford Mountain.
Used parking area off Axford Rd (parking for Wildlife Management Area). Hiked total of 3 miles round-trip for loop first up County House Mountain, then to Oxford Mountain, and then back to parking area. Second of five peaks for the day.