Administrative overhead is defined as resources devoted to activities not directly producing organizational outputs, principally supervision or vertical overhead and administration or horizontal overhead. A brief review of previous studies on police administrative overhead focuses on their conflicting results and methodological shortcomings. Blau's model is described and applied to data collected by Elinor Ostrom in a survey of all police agencies serving populations living in 80 Standard Metropolitan Statistical Areas selected randomly to represent medium-sized metropolitan areas wholly contained in a State. Of the total sample of 106 central city police agencies, 96 were sufficiently described for inclusion within this study. In this model, agency size is the number of employees, vertical overhead is the proportion of officers who rank sergeant or higher, horizontal overhead is the proportion of employees not assigned to provision of direct or auxilliary services. Agency complexity is measured to reflect the division of labor in the organization. Analysis with this model suggests that police organizations are somewhat different from other governmental bureaucracies. Consequently, classical organizational theories regarding economics of scale may not be applicable to police agencies. The results indicate that agency size has little effect on overhead and that efforts to achieve administrative economy should not focus on the benefits associated with large scale organization. Finally, this study discovered that the two types of overhead performed quite differently. Thus, any examination of agency overhead must be sensitive to the type of overhead under scrutiny. Tables, footnotes, and approximately 20 references are included.