I participated in a thread on this very subject not long ago. Here is the link: forums.catholic.com/showthread.php?t=51296&highlight=tattoos
In response to the Scripture you found, please read verse 27, just before the verse about tattoos:
“Do not clip your hair at the temples, nor trim the edges of your beard.” *Lev. 19:27 *
And Verse 26 commands the people not to eat mean with any blood remaining in it. Verse 19 forbids breeding domestic animals with other species and wearing a garment woven with two different kinds of thread! We have to keep in mind that Levitical law was very strict on many points for reasons we cannot relate to culturally, and not incidentally, for health reasons. Can you imagine how dirty the tattooing instruments must have been back then? Other acts were forbidden because they were pagan practices. Unlike the Ten Commandments, we have to know the context of each of these laws before applying them to life in 2005.
As for Church teaching, I have yet to find (and I have searched) any official law forbidding tattoos. I have to conclude, therefore, unless I discover otherwise, that tattoos are licit provided they do not depict anything inherently sinful.