How to infer from Einstein Equivalence Principle that a test particle should follow geodesic? Einstein Equivalence Principle (EEP) states that

A frame linearly accelerated relative to an inertial frame in special
  relativity is LOCALLY identical to a frame at rest in a gravitational
  field.

And also, from this answer, it is stated that the EEP leads to the deduction that a test particle shall follow geodesic.

The reason that the equivalence principle is central to GR is in the
  fact that you can represent the gravitational field with a metric
  tensor at all--you can replace a force equation with a geodesic
  equation for a test mass precisely due to the fact that the geodesic
  that that test mass follows (or the "acceleration" felt by a Newtonian
  mass) is independent of the mass of that test particle.

But I fail to see how to infer logically from Einstein Equivalence Principle that a test particle should follow geodesic. Any ideas?
 A: One way of stating the EP is that Eotvos experiments should give null results. If test particles don't follow geodesics, then it seems likely to give non-null results of Eotvos experiments.
This is all about the EP, not about GR more specifically. We would like general relativity to obey the EP, but this is vague because the EP is hard to define rigorously. Some more rigorous work on this has been done by Ehlers and Geroch, http://arxiv.org/abs/gr-qc/0309074v1 . Without an energy condition, you can't prove geodesic motion of test particles in GR. I wrote up a lowbrow version of their argument in my GR book, section 8.1.3.
A: From the EEP it follows that if you have a freely falling test particle, then you should be able to define a local cartesian coordinate frame in which:
a) the test particle is at rest.
   b) the physics is locally described by physics in Minkowski time.
In particular in this frame all christofel symbols must vanish on particle worldline. We trivially conclude that in this local coordinate frame the worldline is parallel transporting the 4-velocity of the test particle. Since the 4-velocity is also tangent to the worldline, the worldline is parallel transporting its own tangent vector, the definition of a geodesic.
The EEP thus implies that test particles must follow geodesics.
