I *think* this will work:

dueBefore:"next month" and dueAfter:"yesterday"

(if you want to show all overdue tasks, get rid of the dueAfter part.)

No, it does not show result as expected.

Well it works for me. What is wrong with the results?

It also shows few tasks from next month also.

e.g current month is Dec '09 and today date is 23 Dec '09
Using above search clause, it also show few tasks of Jan '10.