If I don't know whether a staff member has a PhD, should I address her as Dr. in my emails?
I always use Dr. ______ whenever I am e-mailing someone at a university and do not know if they have a doctorate.
If they do have a doctorate, I haven't insulted them.
If they don't, they chuckle and are pleased.
In my opinion it strongly depends on the culture. In Switzerland we use solely "Herr"/"Frau" (Mr/Mrs) to address even professors. If you have a look at the history of the country you get an idea why titles of any kind are somewhat frowned upon. However, in Germany the situation is already different and at least under certain circumstances the title is to be used in the address. In Austria it's even sort of a must as I got to hear. At least some people were somewhat sulky when I failed to do so :)
I do not know what role titles play in other places of the world.
It is not a secret who has a PhD. You should ideally do your research and find out.
If you don't do that you run a risk either way. If they don't have a PhD it's very unlikely to offend, but as Logan says, you aren't doing yourself any favours in creating an impression...