On April 22, 2021, about 1004 mountain daylight time, a Flight Design GMBH, CSTW light sport airplane, N378CT, was substantially damaged when it was involved in an accident near Santa Fe, New Mexico. The flight instructor was not injured and the pilot receiving instruction sustained a minor injury. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight instructor reported they were returning to their departure airport at an altitude of of about 7,500 ft mean sea level when he noticed the oil pressure had decreased and of theother engine indications appeared normal. He climbed to a higher altitude, monitored the oil pressure, and positioned the airplane to fly over a suitable landing environment. The oil pressure continued to decrease and when the pressure reached about 4 psi, the engine abruptly came to a complete stop. The flight instructor made a forced landing on a dirt field about 8 miles south of the airport. During the ground roll, the nose wheel struck a rock and the airplane nosed over. Additionally, the flight instructor reported that during the preflight inspection the oil level was correct and there were no indications of an oil leak A review of the data provided by the Dynon EMS-D120 device revealed the oil pressure steadily decreased for about the last 25 minutes of flight. About 3 minutes before the off-field landing, the oil pressure rapidly decreased to zero. Shortly thereafter, the engine rpm decreased to zero. Postaccident examination of the airplane revealed that the oil supply line from the oil tank to the oil pump, which supplied the engine, was observed to leak once compressed air was introduced into the line. The leak was in the area where the oil line rested against the exhaust manifold. The damage to the oil line was consistent with it being subjected to heat from the exhaust manifold. The oil line was connected correctly but routed to close to the exhaust manifold.