If you have a stillbirth are you automatically referred to a genetic counselor?

No. Not automatically, because a stillbirth can have an obviously non-genetic cause, such as an umbilical cord accident. When the cause is unknown, a genetic investigation is indicated.
Depends. If there is a clearly identified non genetic reason for the stillbirth then a referral may not be indicated. Otherwise there may be a need to check parental chromosomes, test the baby for inborn errors of metabolism and see a genetic counselor for advice regarding future pregnancies.