To answer your question directly, crime obviously follows population, just like disease or any other human "event" you might be measuring. To directly compare you could normalise both population and crime figures to z-scores, and classify each region as HH, LL, HL, LH, or come up with a way to combine the figures, but I think to answer your question you need to change what you are asking slightly.
I think you want to understand if there are clusters of criminal activity, taking into account the population. Which would mean you would be interested in clusters of the "proportion or rate of crime". Proportions and rates are different, but the simple answer is the proportion which is the number of crime events divided by the population for the same region and period. Applied Spatial Statistics for Public Health Data (Walter, 2004) gives a good overview of the difference between rates and proportions and their applications. Application to crime would be a little different, someone can be assaulted more than once in the same region, but they can't get the same disease twice, although perhaps murder is an exception. The devil is in the details and what you ultimately want to get out of your study.
Next you need the statistical tools to identify clustering or otherwise in your regions. First you need to look at global indexes of spatial autocorrelation, such as Moran's I and Geary's C. The global indicators do have a slightly different meaning, Moran's I is related to spatially weighted covariances, and Geary's C is squared differences. In their basic form, Moran's I is better suited to population studies and Geary's C is better for sample studies, but either can be adapted to the other role (although I suspect few GIS would implement this-I read about it in fairly contemporary literature).
Subsequently you should look at local indicators of spatial association, like local Moran's I and Getis Ord's G and G*. The location indicators are more focused on identifying which spatial units are significantly clustered for low or high levels of crime, or the inverse (think of a spatial unit with low crime surrounded by high crime and vice versa).
All of these statistical tools have associated methods to measure confidence associated with them, so that you can say that the proportion of crime in a particular region is/is not significantly strongly/weakly clustered/uniform. ESRI have a number of pages describing these types of statistics, but there is some really good contemporary scientific literature out about them too. Both ArcGIS and Geoda have some forms of these statistical tools.
