Hi Linda,
I think you'd need to use the same approach, but unless you have some sort of cross-walk column (something with joinable information in both), you may have trouble getting this to work as it currently exists. I'm not sure what Shape_STAr field you could join with in the shp file...is that a location (UTM or coordinate field)?
Any chance there's another (third) table of data with metadata or spatial data that you could use to join to the two you sent? If so, you could use the (third) data table that has some replicable field with both your shp and the agencies, and then join (or crosswalk) to one or both of the tables as you need.
Another option would be getting the agency jurisdiction info from another shapefile and joining by agency (check out CPAD or CA land ownership...they have pretty detailed info you might be able to use). You could also try using something like you mentioned earlier, the "over()" function if you have two spatial polygon/point files to extract that info.
Not sure what else I can do to help...come by the D-RUG meeting on Tuesday at 10am and we can take a look.
Adios,
Ryan