I gave birth to my daughter April 2016, been living with his father since May 2015 in one roof. He was married and filed tax with his wife since even if they don’t live together.. October 2018 they agreed to process divorce. Should I file tax as common law with my daughters father even if I did not allow him to sign in my daughters birth certificate but we live same as normal married couple? Will I be questioned by CRA with my previous tax returns as I have filed single.
Your best course of action is to contact CRA directly about your situation but I can share the tax rules that apply.
Because the father of your child was residing with you when your child was born, you were (in CRA's eyes) a common-law couple as of that time. That means you and your child's father should have been filing as common-law starting back in 2016. (Birth certificate signatures don't really matter since you fit the description of a common-law couple for tax purposes.)
Your child's father should have been filing as common-law with you as the spouse starting in 2016. This can be corrected by filing an adjustment to his previous years' tax returns but that adjustment must be made by him - you can't file it on his behalf. This would also mean you would have to adjust your previous returns to reflect that he was your common-law partner.
The common-law status is very important to CRA for a number of reasons including the calculation of benefits program such as the Canada Child Benefit. CRA requires that a change in your marital status be filed no more than a month after the change so the updates can be made to your benefit payments.
Bottom line - if you are living as a common-law couple, you should file as one.