If you want to work in Law Enforcement, you will want to err on the side of caution when it comes to having visible tattoos. That means, don't do it! Each agency has their own policies. Some agencies have become more flexible about such things, but many have not. Change happens slowly! Some might allow one or two tattoos, not to exceed a certain size, etc.
So, this would mean the obvious places are out- arms, face, neck. But also consider you might have to wear shorts in the academy, or if you are on bike patrol, so I wouldn't do the legs either!
It's a small sacrifice to make if you really want that career. Once you get on with your first agency, and learn their rules, you might be able to get more tattoos. But, keep in mind, if you ever change departments, it can again become an issue. If the first agency that offers you a job doesn't allow tattoos, be careful before turning down the job. If it is a good agency, take the job, work there two years, and move on.
Sorry this isn't what you wanted to hear, but, I would really hate for you to hurt your chances of being hired!
A bunch of officers I work with have tattoos and come from all walks of life. Each department will have specific policies regarding what they consider acceptable. Like Miss Wasyk mentioned most police departments have strict policies against racist or vulgar tattoos. Think about why you want to join the law enforcement profession and think about the placement of tattoos. Neck tattoos or face tattoos can be a deal-breaker even if they are not vulgar or racist.
I hope this helps.