In this paper, we consider transmission of two correlated Gaussian sources to two receivers through a two-user Gaussian Z interference channel (Z IC). To facilitate our study, we first investigate Gaussian multiple access channels with correlated Gaussian sources and a single distortion constraint at the receiver. Lower bounds on the distortion as well as several achievable schemes are proposed. In particular, a hybrid digital analog transmission scheme is proposed whose achievable region is resolved through coupling it with the quadratic Gaussian CEO problem. These lower bounds and achievable schemes are then applied to the source channel communication over a two-user Gaussian Z IC to derive inner and outer bounds for the distortion region. We conclude this paper by giving a sufficient condition for sending a correlated source over a general Z interference channel.