no, but you can't.
see links below
In this case even if both have agreed that the husband would relinquish his parental rights , then there is no need to support the child even in texas.
Arrears and current support, also, unless/until the child is adopted.
If you relinquish your parental rights, you are still not going to get child support payments. The child support is for the child.
You can't fully relinquish your rights until that back child support is paid. So you have to either pay it first or the custodial parent voluntarily waives it.
If the child is being adopted, not otherwise.
Yes, voluntarily relinquishing your parental rights does not excuse you from having to pay child support.
You can still be required to pay child support. see links below
see links below
In general, parental rights are terminated either preparatory to an adoption, or after a trial in which it is determined that the parent is unfit. In any case, termination of parental rights does not, in itself, terminate child support.
When you relinquish your parental rights so the child can be adopted you are no longer responsible for paying child support. You are liable for support until/unless child is adopted.
Relinquishing one's parental rights does not terminate one's child support obligation.
Basically, you can't do this. You cannot unilaterally relinquish your obligation to provide support for your child.