I'm married filing separately but still live in the same household as my spouse. I'm claiming our child as a dependent but I need to know how many allowances to put?

There are no personal allowances on a tax return.  That was removed from the tax code after tax year 2017.

Thank you. NC Tax Witholding form requested the information.

There's no simple way to answer that. You have to work your way through the  complicated form NC-4.