Inappropriate disclosure of human genomes may put the privacy of study subjects and of their family members at risk. Existing privacy-preserving mechanisms for Genome-Wide Association Studies (GWAS) mainly focus on protecting individual information in case-control studies. Protecting privacy in family-based studies is more difficult. The transmission disequilibrium test (TDT) is a powerful family-based association test employed in many rare disease studies. It gathers information about families (most frequently involving parents, affected children and their siblings). It is important to develop privacy-preserving approaches to disclose TDT statistics with a guarantee that the risk of family re-identification stays below a pre-specified risk threshold. Re-identification in this context means that an attacker can infer that the presence of a family in a study.