If this website is right (
http://www.turtlepuddle.org/american/cooter.html), it sounds like she is initiating things, though I don't think she realizes he's not her breed.
Reproduction
As with the other basking turtles, the males tend to be smaller than females. Males sport long straight claws which are used as part of the mating dance. After detecting what may be a pheromone signal while sniffing at a female's tail, a male river cooter will court a female by swimming above her, vibrating his long nails and stroking her face. Females have also been observed doing this to initiate courtship. If the female is receptive, she will sink to the bottom of the river and allow the male to mount for mating.
Mating takes place in early spring. Nesting usually occurs from May to June.
Another website says that RES (Trachemys) can cross with Pseudemys, Chrysemys, and Graptemys, though not a lot is known about cross-breeding. Considering they are technically different breeds, it is possible that the eggs won't be viable, the hatchlings will be genetically ill, or sterile. (Think horses + donkeys = mules + hinnies. Mules are almost always sterile.) I don't think an actual genetic study of turtles and various species has been conducted, so I don't know how many chromosomes each species has.
