Turtle laid an egg? Or not?

Okay so we have a Red Eared Slider whom we thought was a boy. However, we noticed something weird in "his" tank tonight which looked like an egg. It was white and oval but very thin, almost just like a membrane? Also, this is an inherited turtle from my step brother...this turtle has never laid an egg before so thought it was male. Anyways...can female turtles lay eggs without the presence of a male? Also why would it be the first time she laid an egg? If not an egg, what could it be?