  We show that for complex analytic K3 surfaces any torsion class in
H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group
equals the cohomological Brauer group. For algebraic surfaces, such results go
back to Grothendieck. In our situation, we use twistor spaces to deform a given
analytic K3 surface to suitable projective K3 surfaces, and then stable bundles
and hyperholomorphy conditions to pass back and forth between the members of
the twistor family.
