Are you qualified? That question has much more to it than military service and college education (credit, drug use, driving record, criminal record,...). But a BA and prior service is a great start. Take a look at some of the stickies at the top of the page.
Not sure why you think there are many people quitting CHP. Retiring is much more likely. I run into very few laterals from CHP at other agencies. It is a large state-wide agency with a variety of assignments and possible duty stations. Plenty of benefits in that light.
Can't really comment on any pro/con argument between CHP and local dept without knowing what local dept. There is a huge variability between local PDs and SDs even when they are adjacent. Example: Orange County SD is a full service agency that provides police services to about half the county, the airport, courts and harbors. Just about anything you want to do in LE, you can do at OCSD (investigations, undercover, K9, full time SWAT, bomb squad, pilot, motors,...). There are several depts in the county with around 30 sworn with a very limited number of 'special assignments' that are typically on rotation (3-5 years on assignment then back to patrol). Then you have larger agencies (200-500 sworn) that are somewhere in between. Plus and minus to both depends on what you want out of this career.
As for using your geography degree, that comes down to your articulation and application. I don't know of any "geography" positions in local state agencies. Closest maybe be in crime mapping/analysis but they don't post for geographers. You can always spin the degree to meet the needs of positions. I know a collision reconstruction guy that has a science degree. He positions it as having years of advanced math and physics being applicable to the assignment.