This is an interesting question that have not previously come across. Assuming that the child is a minor and is not emancipated I am not aware of any law that would prevent a parent from withholding the social security card or the birth certificate. Such a withholding could be a perfectly appropriate exercise of parenting if the parent wished to forbid the child from traveling or getting a job. That said, I am not aware of any reason that the child or other parent couldn't march down to the vital statistics office and request a new birth certificate. The same is true for requesting a new social security card.
Why does the minor child need the social security card or birth certificate anyway? Know that both these documents are records that can be obtained from public agencies. You can get a copy of your birth certificate from the office of vital statistics in the state you were born in. You need to check the requirements to order a copy. You may need to be 18. You can get a replacement social security card from the social security office. Don't know if there is an age requirement. I lost my social security card years ago but I had written the number down and memorized it. These day's I don't need it unless I seek a job but I am self employed. I can get it replaced when I need it.
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I agree with the answers above, but I think the real question was supposed to be: Is there any way for an adult child to punish or take action against a parent who has retained their social security card or birth certificate? And the answer to that is, probably not. I can't think of any way that would be worth the trouble. It'd be much easier just to get new copies.
A more serious consideration might be this: If the relationship between parent and child is so bad that this has become an issue, then there's some concern that the parent might use the child's vital information in some inappropriate way. I've seen this happen before - parents running up debt in their children's names, things like that. The child may well want to change their social security number, as well as getting a new set of documents. There's a procedure for this, in the event of suspected identity theft. You can start reading about this here: http://ssa-custhelp.ssa.gov/app/answers/subtopic/c/16,58
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