We have examined muon data collected with the IMB (Irvine-Michigan-Brookhaven) proton-decay detector in search of a muon flux associated with the x-ray binary Cygnus X-3. A sample of 3.6 x 10/sup 4/ muons from the direction of Cygnus X-3 during the period September 1982 until April 1984 shows no evidence of its characteristic 4.8-h periodicity. In the phase interval 0.65 to 0.90 where a signal has been reported by other workers at a similar depth we obtain a 90%-confidence-level limit to the flux of 6.9 x 10/sup -11/ cm/sup -2/sec/sup -1/ for a depth of 1800 m water equivalent. This limit does not conflict with the reported signal. Three subsets of the data taken during Cygnus X-3 radio bursts have been separately analyzed. We find some evidence for an excess in the phase interval 0.50--0.60 at the time of the October 1983 outburst. We examine this excess in detail.