  Over forty years ago, Goethals and Seidel showed that if the adjacency
algebra of a strongly regular graph $X$ contains a Hadamard matrix then $X$ is
either of Latin square type or of negative Latin square type. We extend their
result to complex Hadamard matrices and find only three additional families of
parameters for which the strongly regular graphs have complex Hadamard matrices
in their adjacency algebras.
  Moreover we show that there are only three distance regular covers of the
complete graph that give complex Hadamard matrices.
