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If you are married then you can do it alone with proof of marriage however if you r not married the father must be present to sign as well. If your asking about adding him as a the father on the original and first birth certificate, if its updating/changing a preexisting one then I have I'm not sure x
No the father has to sign it in front of an official like a judge or solicitor.
I thought had to be done by a court of some sort I might be wrong if I’m thinking of wrong thing