My fiance and I live together he pays the bills and makes more money than I do. We had a baby last year who should claim the baby as a dependent?

[alextpant]

He makes about $88,000 a year and I make around $20,000 a year

[xmasbaby0]

If you are a non-married couple who live together with your child, then only one of you can claim the child(ren) and the one not claiming the child does not enter anything at all on their tax return about the child.   The “sharing” of child-related credits you may have heard about is only possible between divorced or never married parents who live apart and share custody and who have a written agreement to share the credits.    The child’s SSN can only be entered on one tax return.   Any other return with the child’s SSN on it will be rejected.   If you are a family, then work out how to share the refund between yourselves.

Prepare the returns both ways to see what works better.   But since you clearly did not pay for over half the household expenses, you would have to file Single --- not Head of Household.   

[MinhT1]

As you are not married, you have to file two separate returns.

One of you (usually the person with the higher income and considered as paying more than half of the costs of keeping up a home) will file as Head of Household and claim the child.

The other person will file as Single.

[Mike9241]

My opinion is that from a tax standpoint, it's probably better for him to claim the child. This way, he gets head-of-household tax rates, which results in lower taxes than if he filed as single. You would then use the single tax rates, but with a much lower income, your marginal tax bracket would probably be significantly lower than his. 

However, we know little about your family's overall tax situation. Certain tax credits may be available. Some can only offset the taxpayer's tax liability, while others may be partially refundable (the credit exceeds the taxpayer's tax liability). The two most common are the Dependent Care Credit and the Child Tax Credit. Each of you might be able to make tax-deductible contributions to tax-advantageous plans like IRAs or HSAs. 

Unfortunately, online only allows one person's return per account. Thus, when you do your taxes online, you will each need a separate account. There are online tax calculators, but I'm not sureof their accuracy