To confirm the previous observational results of Pluto's atmospheric CO in the J = 2-1 rotational transition, we conducted a new observation of CO (J = 3-2) in Pluto's atmosphere in 2014 August with the Atacama Submillimeter Telescope Experiment 10 m single-dish telescope. In contrast to the previous observational result obtained with the James Clerk Maxwell Telescope in 2009 and 2010 by using the J = 2-1 transition, no emission structure was observed near the rest frequency in our attempt. Possible explanations for the nondetection result of the J = 3-2 transition are discussed.