16 Isn't Necessarily Sweet

If you are asking whether a 16 year old is old enough to make permanent decisions, please understand that external voices of authority are not going to reflect what you already know in your heart-of-hearts. Also know that there are no "permanent" decisions. Tattoos can be removed by Laser or skin graft, but of course there will be cosmetic consequences. The laws in many places allow for certain decisions to be made by 16 year olds, but these laws often do not reflect the values of caring parents. For example, in Florida, a 16 year old can lawfully engage in sexual intercourse with someone up to the age of 23. Age 18 is required for relations with someone older than 23. But I digress. 

If your daughter's familial values, like not wanting to displease her father, are stronger than peer-based social values, she will put her tattoo on hold for the time being. Do not be surprised if she is unwilling to comply with your desire however. It is not so much disrespect for you as it is the overwhelming nature of adolescence, in which the primary focus is self-identity. Tattoos are not the same social indicators that they were in previous generations (e.g., drunken sailors on shore leave, convicts, and generally speaking, 'rough trade' individuals). Perhaps discuss the kind of tattoo with your daughter, where she wants to have it, and consequently, who she expects to see it. A tat that will prohibit elegant formal wear later in her life (e.g., plunging back gowns) should be pointed out to her, as well as visibility to conservative employers that may well prejudice them.

At the same time, this conflict is a foreshadowing of your daughter's legal emancipation at age 18, where she will not require parental permission to get tattoos and piercings. Choose your battles carefully, and determine how much 'ego' you want to put into this beyond the attention to details that I suggested above. At this point, Dad is going to have to begin to let go of his parental control. Whatever internalized respect your daughter has for her father is going to have to kick in. She may proceed against your wishes, and regret it later, but she is rapidly becoming an autonomous young adult. Express your wishes clearly, but temper your preference with a measure of detachment.