See below - The credit is nonrefundable. So, if your tax liability is zero, this credit will not produce a refund.
At-Home Parent Tax Credit (code 01)
UC §59-10-1005
An at-home parent may claim a nonrefundable credit of $100 for each child 12 months old or younger on the last day of 2018.
https://incometax.utah.gov/credits/at-home-parent