As a new worm drive, planar tooth internal gear enveloping crown worm drive is composed of a planar tooth internal gear and a crown worm generated by the planar tooth internal gear surface. It is characterized with small size, light weight and high power density, and has wide application prospects on the special service overloaded transmission areas with the size and weight restrictions. In order to grasp the accuracy theory of planar tooth internal gear enveloping crown tooth surface, the mathematical model with process errors is established based on the differential geometry and meshing theory, and the data collection methods are analyzed based on the gear measuring center. The probe radius compensation principle and tooth match method are studied, as well as the optimization of tooth surface errors tracing is proposed. The experiments of tooth surface errors measuring and errors tracing are carried out, and the feasibility is verified. This study is expected to give theoretical guidance to the accuracy assessment and high-precision amend manufacturing of planar tooth internal gear enveloping crown tooth surface, and it is propitious to the promotion and application of internal gear enveloping crown worm drive.