By Barbara Liston

ORLANDO, Florida (Reuters) - The family of Trayvon Martin, the unarmed black teenager killed by Florida neighborhood watch volunteer George Zimmerman, called on Thursday for access to Zimmerman's confidential medical records if a judge approves a request for access to their son's school transcripts and other private documents.

Debra Nelson, the judge who set a tentative June 10 date for Zimmerman's second-degree murder trial, could approve a defense request for Martin's school and social media records at a hearing scheduled for Friday.

Prosecutors want the judge to seal any records obtained by the defense until the court decides whether the defense is entitled to those records, and whether they should be made public.

"George Zimmerman's medical records are far more relevant than Trayvon Martin's school records. They go directly to his state of mind when he pulled the trigger and took Trayvon's life," Ben Crump, lawyer for Trayvon's parents Tracy Martin and Sybrina Fulton, told Reuters on Thursday.

Prosecutors have said in court filings that Zimmerman's lawyers were on a "fishing expedition" for background information about Martin that could potentially be used "to influence public perception or otherwise curry favor with potential jurors".

Mark O'Mara, Zimmerman's lead defense attorney, has said his records request was part of a well thought out plan to focus on potentially relevant and admissible information.

At the same time, O'Mara has sought to block a prosecution request for the release of more of Zimmerman's medical records, citing what he describes as his client's right to privacy.

Martin's school records could provide details of any history of disciplinary action. At the time of his February 26 death, in a gated subdivision in the central Florida town of Sanford near Orlando, the 17-year-old was staying at his father's fiancée's town home.

He was serving a 10-day suspension from Miami's Dr. Michael M. Krop Senior High School after being caught with a baggie containing traces of marijuana.

MEDICATIONS

Zimmerman's medical records could shed more light on the medications he was taking at the time of the shooting.

In a report filed by the Sanford Fire Department and included in discovery documents released in May by prosecutors, paramedics listed Zimmerman's medications as Librax and Temazepam.

Librax is used to treat stomach ulcers and irritable bowel syndrome, and relieves anxiety. Stopping the drug suddenly has been linked to withdrawal symptoms such as anxiousness, sleeplessness, and irritability.

Temazepam is an immediate-acting drug used for the short-term treatment of sleeplessness and includes anti-anxiety, anticonvulsant and muscle relaxant properties.

A report by Zimmerman's doctor made public in July on O'Mara's website shows Zimmerman was also taking Adderall, a psychostimulant used for treatment of Attention Deficit Hyperactivity Disorder, and Omeprazole, a treatment for gastroesophageal reflux disease.

"Knowing what psychological illnesses George Zimmerman had is crucial in understanding his mental state the night he shot and took the life of Trayvon Martin," Crump said.

Zimmerman has said he acted in self-defense on February 26 when he shot Martin, who was walking back from a convenience store to the town home where he was staying with his father.

O'Mara has said he would seek to have the murder charge dismissed in a hearing in April or May under Florida's Stand Your Ground law, which allows individuals in fear for their life Zto use deadly force in self-defense.

However, prosecutors argue that Martin would be alive if Zimmerman had followed instructions from a police dispatcher not to pursue Martin and instead wait for officers to arrive. Prosecutors contend Zimmerman profiled Martin and then pursued, confronted and killed him.

(Editing by Tom Brown, Cynthia Johnston and Andrew Hay)