It is alleged the attack happened on Friday night.
The court heard the alleged victim told police she was out with friends and had consumed half a bottle of vodka and a quarter bottle of rum.
The boy denies the charge. He was released on bail until May 23rd.
Around 18:30 GMT on Friday evening she went for a walk with the accused and he started kissing her on the neck.
A short time later he ripped her tights and they fell into bushes. She claims she was then raped by him.
The detective constable told the court that the girl told the boy to stop and said she did not have the ability to fight him off.
Two police officers later observed that she was upset and crying and in pain from the injuries she sustained.
She had injuries to her back, buttocks and upper thighs and bruises on her arms.
The police officer said these were consistent with attempts to hold her.
The boy told police he had drank four bottles of beer but was not drunk and said the girl had been slurring her words but could walk and talk.
He said he engaged in sexual activity with her but did not rape her. He claimed the girl "didn't say no." He said her injuries were from the fall.
The detective constable told the court the injuries sustained by the girl supported her account. Her injuries were consistent said the detective with "no consent" being given.
She said this was a case where the accused had "led a drunk girl off by herself to rape her."
A defence solicitor said the accused, who was a student, had fully co-operated with police and had not attempted to flee.
Despite objections from police the boy was released on bail. He must not take alcohol and be subjected to a curfew.
He was also ordered not to have any contact with the injured party or any witnesses.
A 15-year-old boy has appeared at Londonderry Magistrates Court charged with raping a 17-year-old girl in the city.