From my own experience, and from those I’ve worked with, a lower RHR is usually a sign of severe over-training, whereas an elevated RHR is an early indicator.

Phil Maffetone has some good material on this subject.

According to this link, overtraining can apparently result in either an increase or decrease in resting heart rate, depending on whether the sympathetic or parasympathetic autonomic nervous system is implicated:
http://www.rice.edu/~jenky/sports/overtraining.html

I have a friend who experience a dramatic drop in RHR due to overtraining as a cyclist. It ended up causing a serious cardiac condition, which took time to reverse.

In any case, rest is a good thing to be sure we don’t overlook.

As a long time athlete, I’ve noticed the best way to protect against over training, is to measure my morning RHR.

If my morning RHR is elevating, it’s a good sign I’m over training. Which is often verified within a few days if I don’t slow down. I always wear a heart rate monitor when training, and if I ignore my elevated RHR, I will next notice I reach my target HR at a lower intensity.

Ignoring that signal usually leads to illness or injury.

This same signal might also be helpful in such adaptation training as cold showers.