Are you sure it is constipation? I know in your other post you said your turtle was male, are you sure? If you have a female she might need to lay eggs. Female turtles will lay eggs even if they are not fertilized by a male. Is she having any other symptoms? Kicking her back legs, trying to get out of the tank? It is possible if you have a female which I can't tell by the picture that she is egg bound. A vet visit would be in order because it could be deadly if not dealt with.
Years ago when your turtle passed something that looked like a small stone, it could have been a stone. Do you or did you have gravel in your tank? If so it is possible that your turtle ate some gravel and passed it.