We have repeated the experiment of Taleyarkhan et al. [Science 295, 1868 (2002)]] in an attempt to detect the emission of neutrons from d-d fusion during bubble collapse in deuterated acetone. Using the same cavitation apparatus, a more sophisticated data acquisition system, and a larger scintillator detector, we find no evidence for 2.5-MeV neutron emission correlated with sonoluminescence form collapsing bubbles. Any neutron emission that might occur is at least 4 orders of magnitude too small to explain the tritium production reported in Taleyarkhan et al. as being due to d-d fusion. We show that proper allowance for random coincidence rates in such experiments requires the simultaneous measurement of the count rates in the individual detectors.