I've kept painted turtles and red earred slider turtles with
koi and they get along fine.

Turtles need a heavy duty filter system, they seem to make lots of
waste.
They will also chomp on plants so you need a heavily planted pond (I
grew water hyacinth in my filter and tossed extras in the pond).
Younger turtles will eat fish, if they can catch them. The younger the
turtle the more they will eat both plants and animals. Older turtles
eat more plants.
Turtles also need a safe place to sun bath every day, for hours at a
time. The area needs to feel sheltered and it has to be easy to get to
(your average turtle not being to agile.. ;-)
They like to eat koi chow. One of my turtles would get right into the
middle of a koi feeding frenzy and gave as good as he got.
I have an island in my pond and that was where I would toss treats for
the turtles only. They loved garden snails.
Lastly, turtles, like koi, need a hole open in the ice during the
winter.

good luck!
kathy :-)