Likelihood calculation for pedigrees is complicated and often time-consuming. Testing correlation structures due to familial aggregation is therefore a preliminary procedure. A score statistic is given to check correlations between relatives of randomly chosen pedigrees. This statistic can be used for quantitative and dichotomous data. For both data types, the distribution of the statistic under the null hypothesis is derived. To demonstrate the performance of the statistic, results of simulations under various models are given. Finally, the test is applied to data on a continuous blood factor.