The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strength of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently, inaccurate estimates of the Godambe information translate in inaccurate p-values. The approach based on a fully nonparametric saddlepoint test statistic derived from the composite score functions is shown to achieve accurate inference. The proposed statistic is asymptotically chi-squared distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies.