You can write a notarized letter indicating you permit the person to care for your child in the event you are unable to do so. You may also want to sign permission for that person to be able to communicate with your child's school and/or daycare as well as obtain medical care and communicate with doctors as needed. If you want, the letter can be filed with the court, but it is not legally necessary to do so. If the child's other parent has custody rights, they will need to sign the notarized letter as well.