This article proposes a systematic method for the optimal design of sensor locations for an automated Coordinate Checking Fixture (CCF). The fixture can be employed for making at-machine assessments of the dimensional accuracy of manufactured components. Coordinate measurements obtained by the sensors built into the fixture can be utilized in estimating geometric parameters of a manufactured part. Two important issues that arise in the design of a CCF are the optimal number of sensors to be used and the best locations for each sensor. The proposed method uses statistical analyses of the Fisher information matrix and the prediction matrix to obtain an optimal set of sensors from an initial candidate set. Sensors are placed at locations that maximize the determinant of the Fisher information matrix for best parameter estimation, while the sensor of the least contribution to the measurement objective is iteratively eliminated. With the benefit of physical insight, the design procedure results in a balanced decision for the ultimate placement of sensors. The developed method also addresses the problem of selection of part locators for part localization in the CCF. Examples are provided for illustration of the developed procedure for automotive space frame extrusion parts.