Motivation: Cutting the cost of DNA sequencing technology led to a quantum leap in the availability of genomic data. While sharing genomic data across researchers is an essential driver of advances in health and biomedical research, the sharing process is often infeasible due to data privacy concerns. Differential privacy is one of the rigorous mechanisms utilized to facilitate the sharing of aggregate statistics from genomic datasets without disclosing any private individual-level data. However, differential privacy can still divulge sensitive information about the dataset participants due to the correlation between dataset tuples. Results: Here, we propose GenShare model built upon Laplace-perturbation-mechanism-based DP to introduce a privacy-preserving query-answering sharing model for statistical genomic datasets that include dependency due to the inherent correlations between genomes of individuals (i.e., family ties). We demonstrate our privacy improvement over the state-of-the-art approaches for a range of practical queries including cohort discovery, minor allele frequency, and chi^2 association tests. With a fine-grained analysis of sensitivity in the Laplace perturbation mechanism and considering joint distributions, GenShare results near-achieve the formal privacy guarantees permitted by the theory of differential privacy as the queries that computed over independent tuples (only up to 6% differences). GenShare ensures that query results are as accurate as theoretically guaranteed by differential privacy. For empowering the advances in different scientific and medical research areas, GenShare presents a path toward an interactive genomic data sharing system when the datasets include participants with familial relationships.