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Cross Object Formula to pull email address from Case

I need to match a pickvalue with Contact First name and  if matches I need to populate that contact's email address into the formula field.
I tried creating a formula text field with IF (ISPICKVAL(Object1.Group, Contact.Fname),Contact.email, "")  but I am getting the result I wanted.
How  can I access the email address from Contact table if Contact Fname or Lname maches with a pick value on another object??
Please help.