Please sign this for a simple change in an outdated law (1953). If your partner dies before your child is born there's no problem putting the deceased person's name as the father if married, but if unmarried, proof (e.g. DNA testing) is required. As it's a serious offence to lie on a birth certificate, there should not be any burden of proof on the mother, especially at a time of grieving.
Joana's long-term cohabiting partner and father to her child died suddenly three weeks before the birth of their second child. As they were unmarried, she was obliged to prove her child's parentage upon the father's death. It was a costly and lengthy legal process, including providing DNA evidence.