Historically, there has been a failure to recognize the complexity of the relationship between crime and the police. This study is based on the proposition that not only do police affect crime through a deterrent process, but also that police services are affected by the rates of crime. From a total of 420 cities with 50,000 or more residents, data were available for 382 which provided the sample for analysis. Data were acquired from the Uniform Crime Reporting program of the FBI, the County and City Data Book for the 1970 census, and the Municipal Year Book of the International City Management Association for 1971. Actual levels of police presence, operationalized as per capita patrol units, served as a crucial variable in the model, linking the police to deterrence theory. Analysis revealed that police presence was a function of the numbers of police employed and the nature of departmental policy in regard to the deployment of two-officer units. Clearance rates for the various types of crime were generally not found to be a positive function of police presence, with auto theft and rape as the only exceptions. Thus, levels of police presence in the form of per capita patrol units were not found to be determinants of clearance rates. Findings of the study do not support the traditional concept of a deterrent effect of police presence. Strong support was found for the proposition that crime generates citizen demand for more police, indicating that such demand originates primarily with violent types of crime. Perceptions of potential offenders concerning levels of police presence and punishment probability should be introduced in future models of police-crime relationships. One figure, 1 note, 4 tables, and 27 references are provided.