Dear Madam/Sir, Could you please let me know? What is the requirement, do we have to file both federal and state taxes? Or only federal are compulsory? Thank you.

Yes, You need to file both.

As far as I know, both federal and state tax returns are required, unless you live in a state that does not have state income tax, in which case, there is no state tax return to file. But I should add the obligatory disclaimer that I am not a tax attorney and you should consult a tax professional

If you don't owe any state tax, how will the state know that you don't owe any?  The feds share info with the states, and if you don't send in your state return, you will get a letter and a penalty assessment based on what they think you owe.  No one wants this letter, because it always comes at a time you're not prepared, or have misplaced your info.  You don't want to be in the position of having to defend why you didn't file a return.  It's better to file a return for their information.  To save the cost of e-filing, just mail it in.