When nonrandom segregation of marker haplotypes from parents to offspring is detected, leading to an increased parental haplotype sharing by affected offspring, an association between the disease and the marker loci is often inferred. In this paper, we provide the uniformly most powerful test for testing nonrandom segregation, and compare the power of this test with another test that is available in the literature. Other statistical properties of the two tests are also discussed. Further, since nonrandom segregation can result from linkage of the disease and marker loci, when the hypothesis of random segregation is rejected, it is of interest to estimate the underlying parameter assuming linkage. We provide an estimation procedure.