we propose an overlay cooperative cognitive radio (CR) non-orthogonal multiple access (NOMA) network which has channel estimation errors and imperfect successive interference cancellation (SIC). To further performance enhancement, spatial diversity gains can be offered by relay selection which is chosen based on channel state information (CSI) among the candidate secondary transmitters. We derive an analytical expression of the outage probability of the primary receiver (PR) and the secondary receiver (SR) as a function of the channel errors and imperfect SIC, respectively. And the analytical outage probability expressions are validated through simulations. Numerical results show that when the number of relays (N) is fixed, the performance of the PR degrades as the increase of the channel estimation errors. In the case of N= 2, to satisfy the required outage probability of 1× 10-4, 8.2 dB of the transmit SNR degradation is noticed with correlation coefficient ρ= 0.98 in comparison with ρ= 1. Moreover, the SNR degradation caused by the less correlation coefficient decreases as the number of relays increases. On the other hand, as further imperfect SIC, the error floor that the performance enhancement does not expect with the increase of the transmit power is noticed. The optimum power allocation which maintains the minimum outage probability of SR is realigned by the error floor.