The 35-ton prototype for the Deep Underground Neutrino Experiment far detector was a single-phase liquid argon time projection chamber with an integrated photon detector system, all situated inside a membrane cryostat. The detector took cosmic-ray data for six weeks during the period of February 1, 2016 to March 12, 2016. The performance of the photon detection system was checked with these data. An installed photon detector was demonstrated to measure the arrival times of cosmic-ray muons with a resolution better than 32 ns, limited by the timing of the trigger system. A measurement of the timing resolution using closely-spaced calibration pulses yielded a resolution of 15 ns for pulses at a level of 6 photo-electrons. Scintillation light from cosmic-ray muons was observed to be attenuated with increasing distance with a characteristic length of $155 \pm 28$ cm.