Hi Rob,
I don't know of any that are specifically for tracking emergency services. There is a recently released database from the Fund for the City of New York called
Up & Running that may be helpful. It is developed in Access, and has a feature called "interactions" that allows you to customize the way your organization relates to folks. This could be used as a simple case management system, where you track the stages of providing Emergency Services. There are also a variety of custom fields you can configure outside of this.
The DB is in its first release, which does mean its new and will have some bugs to iron out. But it is free and the code is open source.
Hope this helps!
Eric