WA procedure for determining paternity and obligation for paying child support

I guess it depends on what you want. If she is not suing you for support, and you are not supporting the child, you needn't do anything unless you believe the child is yours and you want parental rights. If you want to be the father then ask for a paternity test in court (usually done in a family court)
If she is seeking support, again you have a right to admit the child is yours or you can seek to have paternity established with a test.
If she is telling everyone that the baby is yours and that is a lie, and it has in some way effected your standing with people in the community or at work then you can sue her for defamation of character and seek an order that she not speak that again. It will also probably require a test as Truth is an absolute defense to a defamation action.

Good luck