There are two restrooms in Yume Nikki, found in Block World, and Graffiti World. Using a restroom doesn't do anything except allowing the player to hear a flushing noise when Madotsuki is done. You cannot go inside with the Bike, Severed Head and Umbrella Effects.
Block World
There is a male restroom in eastern Block World. Despite being a male restroom, Madotsuki still uses it like any other one.
Graffiti World
There is a female restroom in the Graffiti World. Once again, Madotsuki uses it like normal, accompanied with a flushing sound effect.
Speculation
In the game, Madotsuki can use both male and female restrooms. This has lead to some controversy regarding Madotsuki's gender with some claiming that Madotsuki may be transgender. For more information, please visit the Theories page.