The strategy of contact coordinate measurements of free-form surfaces may include many elements, e.g. methods of the distribution of measurement points, which determine the final accuracy of measurements. Measurement points, at which contact coordinate measurements are conducted, should be located in the parts of surfaces of investigated objects which are characterized by the poor quality of manufacturing in order to decrease the time of measurements and increase the accuracy of a measurement task. The paper presents the algorithm of determining the strategy of contact measurements in the field of distributing measurement points on curvilinear surfaces. The new method is mainly intended for measurements conducted by using coordinate measuring machines. The algorithm takes into account the results of non-contact coordinate measurements. The application of initial non-contact measurements in the mentioned algorithm is aimed at increasing the accuracy of contact coordinate measurements and speeding up the whole measurement process of complex products.