Genotype imputation has become a standard option for researchers to expand their genotype datasets to improve signal precision and power in tests of genetic association with disease. In imputations for family-based studies however, subjects are often treated as unrelated individuals: currently, only BEAGLE allows for simultaneous imputation for trios of parents and offspring; however, only the most likely genotype calls are returned, not estimated genotype probabilities. For population-based SNP association studies, it has been shown that incorporating genotype uncertainty can be more powerful than using hard genotype calls. We here investigate this issue in the context of case-parent family data. We present the statistical framework for the genotypic transmission-disequilibrium test (gTDT) using observed genotype calls and imputed genotype probabilities, derive an extension to assess gene-environment interactions for binary environmental variables, and illustrate the performance of our method on a set of trios from the International Cleft Consortium. In contrast to population-based studies, however, utilizing the genotype probabilities in this framework (derived by treating the family members as unrelated) can result in biases of the test statistics toward protectiveness for the minor allele, particularly for markers with lower minor allele frequencies and lower imputation quality. We further compare the results between ignoring relatedness in the imputation and taking family structure into account, based on hard genotype calls. We find that by far the least biased results are obtained when family structure is taken into account and currently recommend this approach in spite of its intense computational requirements.