How can we get the date that the project was marked as completed through project status drop down box?

Changepoint does not store this type of history information. In order to get the real date that the project was marked as Completed, a configurable field with history tracking for the 'completed date' can be setup. A  custom trigger or calculated stored procedure should be created to set the date.

Another option is to use workflow to complete the project, since workflow history is also available. There is a 'project cancelled' example in the accelerator database, which uses a stored procedure step to complete the project.