Is it possible to create web service CRUD operations for contributed modules in drupal 7? I have using a privatemsg module for chating in our site,

Privatemsg

Services

Is it possible to do a web service CRUD operations through this module?

any suggestions?
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.