W4 and Tax Return Advice for noncustodial parent

I am a single non-custodial parent paying child support monthly for my child born this year. The custodial parent is not working since Cov-19. 

 

I've read that the custodial parent has to sign F-8332 in order to relinquish claiming the child for this year. 

Does that apply for both W4 withholding and tax return?

 

Or can I still put the child as a dependent on W4 without the parent signing the F8332 and not claim the child in this year's tax return??