On April 28, 2005, at 0935 eastern daylight time, a Piper PA-20, N7053K, registered to Matlad, Inc., and operated by the airline transport pilot, veered off the runway during landing roll at Thomaston - Upson County Airport, Thomaston, Georgia. The personal flight was operated under the provisions of Title 14 CFR Part 91 with no flight plan filed. Visual meteorological conditions prevailed. The airline transport pilot and the passenger were not injured, and the airplane sustained substantial damage. The flight departed Aiken Municipal Airport, Aiken, South Carolina, about 0815. The pilot stated the approach to runway 30 was normal, and the main wheels touched down normally. The pilot stated that, when the tailwheel touched down, the airplane pulled hard to the left, application of the rudder had no effect, and the airplane continued left off the side of the runway. The airplane continued through the grass, and the empennage collided with the runway's precision approach path indicator lights. Examination of the airplane revealed damage to the empennage and fuselage. The tailwheel rudder arm assembly was found fractured and separated on the right side, and evidence of a previous weld repair outboard of the fracture was observed. The weld repair was observed at the thickest area of the tapered rudder arm, and the fracture was observed at a smaller-diameter area. Metallurgical examination of the rudder arm revealed the aluminum component showed deformation near the fracture surfaces with no evidence of fatigue. The pilot stated he had purchased the airplane two days before the accident, and the airplane had accumulated approximately 1.9 hours since annual inspection. Review of maintenance records for the airplane revealed no record of the rudder arm assembly repair.