I have using a privatemsg module for chating in our site,
Is it possible to do a web service CRUD operations through this module?
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Yes, the Services module has an API, details of which you can find in the module files. You can use that API to provide CRUD for anything at all. See Creating a resource for Services 3.x for a full module example.
Since private messages are entities, you might also look to the Services Entity API module for inspiration (or, it you're particularly lucky, a pre-built solution, depends what you need, and whether you can use an alpha release):
This module provides support for all Entity API entity types to Services. All entity types get a standard resource, similar to what Services provides for code entity types such as nodes.