Is a witness's signature on a new-born's birth certificate considered a false testimony if the witness did not attend the actual birth?

A Muslim's testimony is not permissible concerning a matter of which he has no knowledge. However, if he comes to know of a birth through hearsay, his testimony is permissible, even without having been present at the actual event. If he does not have knowledge of it, then his testimony is not permissible. Repentance is achieved through regret, seeking forgiveness, and righteous deeds. "Regret is repentance," as Allah the Almighty says: "And whoever does evil or wrongs himself then seeks forgiveness of Allah will find Allah Forgiving and Merciful" [Quran 4:110], and His saying: "But whoever repents after his wrongdoing and makes amends, indeed, Allah will accept his repentance" [Quran 5:39]. If the testimony resulted in harm, then one must disavow oneself. If there was no harm, we hope that repentance will be accepted without disavowal.