Best answer is NO ... my suggestion is this ... only the person with the higher income should claim the child (and claim married filing status). And the person with the lower income should be claiming SINGLE as the filing status on the W-4 but use the IRS tool to figure this out yourself ... of course there is no requirement you change either W-4 to claim the child so if you like the refund you are already getting then leave things alone.
Use the Tax Withholding Estimator on the IRS web site to figure out what you and your spouse should each put on the W-4 forms that you give to your employers. It's much easier than using the worksheets on the form. It will let you adjust your withholding to get the approximate refund amount that you want.
Tax Withholding Estimator
