Increasing the productivity of high-precision manufacturing requires efficient product inspection, for example, using integrated scanning systems on CNC machine tools (MT). However, measuring the dimensional and shape accuracy of workpieces using a touch probe (TP) on MT is negatively affected by the geometric accuracy setting of the MT, thermal stability of the MT and its surroundings, type of scanning system. The aim of this paper was to examine the possibilities of assessing the capability of touch probe measurements on MT, to define the size of the permissible controlled tolerance of the workpiece and to assess the influence of the geometric accuracy of the machine on the size of the permissible tolerance parameter of the inspected workpiece. In the presented experiments, the calculation of the TP measurement capability is based on a new approach respecting the VDA5 standard extended by the minimum tolerance (TOLmin) conformity assessment procedure according to ISO 14253-1:2017.