On June 25, at 0630 central daylight time, a Weatherly 201C, N1299W, exited the prepared runway surface, following a loss of directional control during a takeoff roll on runway 36 (2,500' X 50', grass), at Grieve Airport (Y-20), near Buffalo, North Dakota. The 14 CFR Part 91 aircraft repositioning flight was departing in visual meteorological conditions for the local planed flight. No flight plan was on file. The pilot reported minor injuries. The airplane sustained substantial damage. In a telephone conversation, the pilot reported that it had rained for 72 hours before the time of the accident. The pilot stated that he wanted to reposition his aircraft to a dryer field because of the existing runway conditions. The pilot reported that there was visible standing water on the runway when he initiated the takeoff roll. The pilot said that during the takeoff roll, "the left main wheel contacted some water on the runway and dragged the airplane left, off the runway to a soft field." Upon reaching the soft field the aircraft nosed over and came to rest on its back.