We report on our search for genetically related asteroids amongst the near-Earth object (NEO) population - families of NEOs akin to the well known main belt asteroid families. We used the technique proposed by Fu et al. (2005) supplemented with a detailed analysis of the statistical significance of the detected clusters. Their significance was assessed by comparison to identical searches performed on 1,000 'fuzzy-real' NEO orbit distribution models that we developed for this purpose. The family-free 'fuzzy-real' NEO models maintain both the micro and macro distribution of 5 orbital elements (ignoring the mean anomaly). Three clusters were identified that contain four or more NEOs but none of them are statistically significant at \geq 3σ. The most statistically significant cluster at the \sim 2σ level contains 4 objects with H < 20 and all members have long observational arcs and concomitant good orbital elements. Despite the low statistical significance we performed several other tests on the cluster to determine if it is likely a genetic family. The tests included examining the cluster's taxonomy, size-frequency distribution, consistency with a family-forming event during tidal disruption in a close approach to Mars, and whether it is detectable in a proper element cluster search. None of these tests exclude the possibility that the cluster is a family but neither do they confirm the hypothesis. We conclude that we have not identified any NEO families.

36 pages, 3 tables, 9 figures, accepted for publication