Hi, I want to re-open the task which i have completed (from My Completed task dashlet) and want to reassign the same task to other user (so that goes inside users My To Do Task dashlet).
As Cheffilet says you cannot re-open a completed task.
However you could create a new assignment with similar values and assign it to someone else.
For advanced workflow you could build the re-assignment steps into your process or have a task with pooled actors which allows one of a pool of people to grab a task and deal with it or put it back uncompleted.
But the bottom line is that a completed task is completed forever.