  We investigate the Markov property and the continuity with respect to the
initial conditions (strong Feller property) for the solutions to the
Navier-Stokes equations forced by an additive noise.
  First, we prove, by means of an abstract selection principle, that there are
Markov solutions to the Navier-Stokes equations. Due to the lack of continuity
of solutions in the space of finite energy, the Markov property holds almost
everywhere in time. Then, depending on the regularity of the noise, we prove
that any Markov solution has the strong Feller property for regular initial
conditions.
  We give also a few consequences of these facts, together with a new
sufficient condition for well-posedness.
