There is no unique relation between BEC and superfluidity. An ideal-ga — Superfluidity

"Superfluid phenomena in liquid helium-4 have fascinated both experimentalists and theoreticians since the discovery of superfluidity in 1938 simultaneously by Peter Kapitsa at the Soviet Academy of Sciences and by Jack Allen and Donald Misener at the Royal Society Laboratories in Cambridge, England. These phenomena include a vanishingly small viscosity, a very high heat conductivity (30 times greater than copper), and many other bizarre effects, such as the He fountain, film flow and creep, and quantized vortices (see the article by Russell Donnelly in Physics Today, July 1995, page 30)."

"This paper presents an attempt of explaining the phenomenon of superfluidity on the basis of the theory of degeneracy of a non-perfect Bose-Einstein gas. By using the method of the second quantization together with an approximation procedure we show that in the case of the small interaction between molecules the low excited states of the gas can be described as a perfect Bose-Einstein gas of certain “quasi-particles” representing the elementary excitations, which cannot be identified with the individual molecules. The special form of the energy of a quasi-particle as a function of its momentum is shown to be connected with the superfluidity. The object of this paper is an attempt to construct a consistent molecular theory explaining the phenomenon of superfluidity without assumptions concerning the structure of the energy spectrum."