Can you be taken to court for not giving a pregnant woman money for doctor visits

A court could well conclude that you acknowledged fathering the child by the fact you paid for care. If you are sure you want to fight to prove the child is not yours, you will have to get a court ordered paternity test. It is up to you. It does tend to ruin the relationship with the mom. If you really like the mom, or think the child is yours, this is your chance to be a father to a child, something many people wish they had. best of luck to you