I have the following suggestion:

Pool the data and compute the covariance matrix based on the pooled dataset, let it be S, if S is positive definite, define V=Ca - Cb, where Ca and Cb are points correponding to the centers of the two clusters, the following quadratic expression can be taken as a measure of the generalized distance between the two clusters:

D(Ca,Cb)= V'*(invS)*V

Hope this is useful.

Thank you Mr. Ghosh. Is Bhattacharya Distance also applicable in this case?

i suggest that you first test the null hypothesis of equality of the co-variance matrices associated with the two clusters, if the null hypothesis is found to be reject-able at given pre-determined level of significance, you go forward with Bhattacharya distance based analysis.

Thank you Mr.Ghosh