I've been in a lesbian relationship with my partner 4 nearly 3 years now, and I've recently had a baby girl. Her dad isn't on the birth certificate so can my partner legally adopt my baby??

Adoption laws vary greatly by state so you will have to check the laws for your state.

Get a lawyer.

It depends on the state--some allow gay partners to adopt, some don't.

Regardless, you will STILL need to have the biological father's permission for an adoption to go through, whether he is on the birth certificate.