According to the 1967 NHRA rulebook: "Exhaust system must be equal to factory equipment per h.p. claimed. Dual exhaust pipes, with mufflers are permitted.
Headers are also accepted, but exhaust must be routed through mufflers and tail pipes. All mufflers must be production type and installed in the stock location with tail pipes extending at least to the rear axle. The main body of any replacement muffler must be at least 19" in length. Open by-passes may be used, but must be installed in front of the muffler and installed in such a manner as to direct exhaust away from the strip, tires, and car body. Outlets for open exhaust cannot exceed 3.5" in diameter. A maximum of two (2) outlets per car permitted. No flexible pipe permitted on any car in competition."
A lot of words but I hope that it answers your question! I'm fairly certain that in 1968 an exhaust system was not required.
Walter