BERLIN—A small plane crashed shortly after taking off in southwestern Germany on Saturday and three bodies were found at the crash site, police said. The Piper aircraft came down in a wooded area near Steinenbronn, south of Stuttgart. The plane took off from Stuttgart Airport on Saturday morning with three people on board and was headed for Magdeburg in eastern Germany. Police said they hadn’t yet determined the identity of the victims, German news agency dpa reported. Germany’s air traffic control agency said the pilot didn’t make an emergency call before the plane disappeared from radar, and the wreckage was located about 20 minutes after it took off. The cause of the crash wasn’t immediately clear, but investigators recovered a flight recorder from the plane.