Windows 10 64b, intel i5 6400
It's broken in 2.78a b76dbf5, 64f5afd,
It works on the stable release and on autobuilds from earlier in the year
Short description of error
Curve segment hairs don't cast any shadow from transparent shaders. It only happens on curve segments, not line segments or triangle.
Open the file in both Blender versions, render and check the results. Alternatively, you can switch to line segment or triangle hairs.
To replicate from scratch, use a transparent shader with semitransparency, or even completely black, i also recommend restricting the transparency shader to the shadows using lightpath node so the effect is more visible when combined with a diffuse shader, like in the example.