Ayan,
I appreciate your direction. The crashes , point features, are "snapped" to the target routes and tested with "Near" to be certain they are within 0.05' of the LRS. So, the search radius is set at that value. The Locate Features tool then executed and table joined back to the crash data. Of course, the crash data now consists of the associated Route ID and Mile Point. Since I need the remaining roadway data attached to the crashes, I use the spatial join tool, however, as discussed above, the spatial join sometimes joins the intersecting roadway even setting the search radius at 0.05. Apologies, but I'm not really following what you are suggesting and don't understand how it would alleviate the problem.