Subscribing to the notion of "Don't overdo it". I have been looking for the right opportunity to initiate casual non-sexual touch. This has been difficult. The first couple of Touches are bound to cause attention and I want them to be natural.
I took a communications class years ago and they talked about the power of touching someone, and talked about the best areas to touch casually to make someone feel more comfortable with you without feeling threatened. The number one spot was the shoulder/ upper back. So perhaps if she is showing you something on a phone, computer or magazine you touch her shoulder while looking at it over her shoulder, that sort of thing. Number two spot was elbow, they were suggesting if you shake hands you reach out with your other hand and lightly touch/grasp their elbow. Can also work if you are talking to someone casually, reach out and touch their elbow for emphasis like "oh and get this...". Touching hands is also OK as long as it's not a hand-holding thing, but done more for emphasis similar to touching the elbow. No face or neck touching, that's getting too personal. Same with lower back, that is reserved for someone you are intimate with. Obviously anything below the waist is off limits.
