In this paper, we consider a hybrid satellite terrestrial cooperative network with a multi-antenna relay where the satellite links follows the shadowed-Rician fading and the terrestrial link undergoes the correlated Rayleigh fading. Specifically, two different channel state information (CSI) assumptions are considered: 1) full CSI at the relay; 2) full CSI of satellite-relay link and statistical CSI of relay-destination link at the relay. In addition, selection combining (SC) or maximal ratio combining (MRC) are used at the destination to combine the signals from direct link and relay link. By considering the above four cases, we derived the closed-form expressions for the outage probability (OP) respectively. Furthermore, the asymptotic OP expressions at high signal-to-noise (SNR) are developed to reveal the diversity orders and the array gains of the considered network. Finally, numerical results are provided to validate our analytical expressions as well as the system performance for different cases.