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You can use the Privileges dialog box in ArcGIS Desktop to do this
When publishing data, you have to think about the privileges of the person doing the publishing (they have to have access to the data to publish it) AND the privileges of the user that is specified in the .sde file you registered with ArcGIS Server. All the services will access the geodatabase data as the user in the registered .sde file.
Therefore, to publish a map service (or any other read-only service), connect permission to the database and select privileges on the datasets are required for:
-The user making the map (or accessing the data to be published)
-The user you have in the Database Connection file (.sde) that you registered with ArcGIS Server.
*Be aware that if you use Windows-Authenticated logins, the ArcGIS Server primary site administrator (that's the administrator account created when you set up the ArcGIS Server site) needs the same privileges: in this case, connect permission and select privileges on the datasets.
And if I understand you correctly, if the owner of the data or the user in the .sde file would like the publish a map service, they both need the permission to connect tot he database and some privileges to the datasets. right?