According to scripture we are righteous not by our doing but by our believing. The Word says "if we confessed with our mouth that Jesus is Lord and believed in our heart that God raised Him from the dead, we are saved. For it is with heart a man believes and is made righteous and with the mouth he confesses and is saved." Roman 10-9-10
I know that in Philippians 3:9 we do not have a righteousness of our own from keeping the law, but one that is through faith in Jesus, the righteousness that is from God based on faith.
I truly believe that I am righteous by my faith in Christ. Which means we have been made right with God by our faith in Jesus Christ payment for us.
So just as a the dogwood doesn't strive to be a dogwood, it just is, so we are righteous by our faith. We do not have to perform or try to be righteous. Based on that belief and our right standing, our righteousness will begin to be displayed in our actions.
This righteousness / right standing with God means we are at peace with God. But since we are already righteous does that give us a right to go on sinning? Paul looked at this in Romans 6 as you can see below.