Spectrum sensing is mandatory in Cognitive Radio (CR) systems, and is used in order to identify spectrum opportunities, and to guarantee that the secondary user does not cause unacceptable interference to the primary user. Since a single relay may be in a fading or shadowing, cooperative sensing among multiple relays which experience uncorrelated fading is required to guarantee reliable sensing performance. In this paper we develop efficient centralized statistical algorithms for cooperative spectrum sensing in a cooperative based cognitive radio network. In order to obtain the optimal decision rule based on Likelihood Ratio Test (LRT), the marginal likelihood under each hypothesis needs to be evaluated pointwise. These, however, cannot be obtained analytically due to the intractability of the multi-dimensional integrals. Instead, we present a low complexity algorithm to perform approximation of the marginal likelihood, based on the Laplace approximation. Performance is evaluated via numerical simulations and compared to lower bounds under perfect Channel State Information (CSI).