cotorro vs cotorra
Would you call a chatty girl a cotorra and a guy a cotorro? Or both cotorra?
Now that's a tricky question... xDD
From my native daily language, I would make the difference between male and female, but it isn't like that. The meaning only comes from the female and the origins are from there so it should be calling cotorra to both genders.
But some people can take it bad to call them as a 'woman' because you are using the female gender...
To answer your question, it should be cotorra for both, but both examples are used in the daily life by spanish people.