This paper presents a new multiple hypothesis problem for spectrum sharing between primary users (PUs) and secondary users (SUs) with cognitive radio technique. The considered four hypotheses are as follows; the studied frequency band is vacant (hypothesis H0), the studied frequency band is occupied only by a PU (hypothesis H1), the studied frequency band is occupied only by another SU (hypothesis H2) and the studied frequency band is occupied by PU and another SU simultaneously (hypothesis H3). Most of the related works have considered the binary hypothesis testing problem (H0 and H1). By applying the multiple hypothesis testing problem, we can enhance the protection of the PU but also fairness among multiple SUs. To avoid difficulties in forming decision regions in the multiple hypothesis problem, a framework where two binary hypothesis tests are combined to form the final decision is introduced. The problem in implementing this framework is that a SU signal can cause interference to the binary hypothesis test for the PU signal (and vice versa), so that we may falsely detect presence of a PU even when only a SU is present. To reduce the leakage due to interference, we propose an implementation using cyclostationary based detection. However, under H3, the correlation between the PU and SU signals is difficult to avoid. We theoretically analyze the correlation under H3 and show its impact on the detection performances.