One easy way would be to create a query and add "Local ID" and "Date of Service" to it.
Uncheck the "Show" box under the "Date of Service" field, you just want this for your criteria. Placed your date criteria under this field, i.e.
Code:
BETWEEN #8/1/2012# AND #8/31/2012#
or whatever your date criteria is.
Then click on the Totals (Aggregate) button in the Query Builder (looks like a Sigma). This will add a "Totals" row in the query builder with the phrase "Group By" under your two fields.
Under the "Date of Service" field, change the value of that Totals row to "WHERE".
Now, if you view your results, it will just return the Local IDs that have had at least one service during that month. If you want to include a count of the number of services, just go back to the Query Builder, and add any field to the query, and change the Totals row value to "COUNT".
You can then join this to your Local IDs table (assuming that you have one), performing a Left Join from your Local IDs table to your Service Count query.
Then you can add a calculated field that will return a "Yes" if the Count for that ID is greater than zero, otherwise return a "No", i.e.
Code:
ServiceCheck: IIf([Service_Counts_Query]![CountOfDate of Service]>0,"Yes","No")