How do I start a new career at 37 when everything I've ever done (and therefore everything on my resume) is geared towards Law Enforcement?

In Law Enforcement, you are a leader, negotiator, team player, communicator, risk taker, first responder, respected, wanted, needed, comfort provider, empathic, quick thinker, decision maker and problem solver. Certain the list can go on and on. Don't sell yourself short-sell the skills you learned and taught! Best Wishes for much continued success.

First you have to decide what to do then spend the time researching what it is that's required. Look some people up who work in that field and ask them. Try LinkedIn for starters.

Then see what that you've done could apply. Think more soft skills if it's a completely different career. Leadership, goal setting, overachieving performance targets, HR management, crisis management, etc.

I'm 47 and about to do the same thing. Good luck.

SSG Steven O'Connor ,
If you desire the Law Enforcement industry, then pursue it. If not, adjust your resume to the industry that you desiring as you will be amazed at the amount of varied skills that you posses but saw it as no big deal because you were simply doing your job on a daily basis. A skill evaluation would not hurt.