If someone has food stamps and they don't know the baby father on their case ... and the father wants to claim the child can you get in trouble for that

[Opus 17]

The IRS does not share your tax information. 

However, it is possible that your state tax department might share dependent information with your other state agencies.  You would have to ask them.

Certainly, getting benefits by lying that you don't know the father, could lead to all kinds of problems down the road.

Also, the father can't legally claim the child as a dependent unless the child lives with him more than half the year, or you give the father a signed release form.  So either you are living together, which is another red flag for the welfare people if you didn't tell them, or the father might claim the dependent illegally on his tax return.

You may want to think this over a bit more before you act.