I don't have SimCity Classic, but I know in SimCity 2000, which I've had for 12 years, there's a square that you can click in the toolbar that will dispatch either policemen or firemen. Clicking and holding will enable you to select either. If you've got a big city with a military base you can send them out too.

I'd check your manual, Maxis manuals were always very well-written and sometimes even humorous.