C.O.
it's very hard to answer this question considering we don't have much information.
Typically it is NOT against the law to run away...however, if the person takes someone else with them and travels across state lines then it becomes kidnapping - I BELIEVE - I am not a cop nor am I a lawyer.
Your granddaughter is 16 years old. She is doing EVERYTHING in her power to exude confidence and independence....she BELIEVES that she is an adult and ready to make adult decisions. Instead of getting mad - you were 16 once too....COMMUNICATE with her. Ask her WHY she feels the need to run away, get tattoos, get emancipated, etc.
Help her with her life skills - can she balance a checkbook? Does she know how to budget money? Does she have a job? instead of holding her back and keeping her a 'child' - get involved. KNOW her friends. Set a good example, LISTEN to her about her wants, needs desires - find out WHY she feels the need to get the chest tattoo....she's going to push your buttons, so instead of "LETTING" her do it - treat her like an adult - set the expectations - tell her - okay - I get it - I hear that you feel you are an adult - show me adult responsibility....show me that you CAN be an adult - budget, balance, get good grades...show me how you want to excel.....