In Leviticus this spoke to the Isrealites at that time, but was a direct command of GOD! However, most people want to say we are under the New Testament so this does not apply to us. I disagree! The New testament was never to remove the Old Testament it was put in place that it might be fulfilled! But, thats a whole other discussion. Although 1 Corinthians 6:19-20 does not directly apply to tattoos or body piercings, it does give us a principle: “Do you not know that your body is a temple of the Holy Spirit, who is in you, whom you have received from God? You are not your own; you were bought at a price. Therefore honor God with your body.” This great truth should have a real bearing on what we do and where we go with our bodies. If our bodies belong to God, we should make sure we have His clear “permission” before we “mark them up” with tattoos or body piercings.
One last point and this one sticks with me as a reason I have never desired to "tatt up" as the kids say! People have also been forcibly tattooed. A well known example is the identification system for inmates in Nazi concentration camps during the Holocaust. Early Blacks of Slavery were tattoed in order to be tracked like merchandise. In todays criminal justice system they love people to have tattos they say its the easiest way to track down and find them as well as convict those who break the law by their own tattos being there main identification! So, while there is no direct biblical reason not to tatto spoken of directly you must judge the legal, moral and values standards you have for yourself!