Telling the difference in the sex of koi fish can sometimes be difficult. It is easiest when they at sexual maturity and during spring/summer.
Female kois are more rotund because their bellies carry a full load of eggs. They have a shorter, wider head and the texture of their skin is smooth all over. The vent will be protruding.
Male kois are more streamlined and elongate. They have longer, narrower heads and the texture of their skin along their flanks and operculae (gill covers) are slightly rough to the touch. The vent of male fish will be sunken/concave.
During the breeding season, you may notice males chasing after females as they spawn.