By Chiara Saldanha

NEW DELHI, July 7 (Reuters) - The deaths of a number of witnesses in a massive fraud case surrounding cheating at college and government jobs has become the latest source of discomfort for India's ruling party, already on the defensive over influence trafficking allegations.

Investigators say thousands of people got jobs or medical degrees from systematic exam cheating that generated millions of dollars in bribes in the state of Madhya Pradesh.

At least 36 people connected to the case in the Bharatiya Janata Party (BJP) run state have died since the scam was first brought to light. More than 2,000 have been arrested in relation to the scam.

Four more people connected to the case have died since the weekend, just days before a Supreme Court hearing and amid opposition accusations that a regional unit of Prime Minister Narendra Modi's party was protecting the accused.

"They are not arresting the real culprits," said Vivek Tankha, a lawyer representing three whistle blowers who exposed the scam in 2013.

State Chief Minister Shivraj Singh Chouhan, a popular BJP leader, denies wrongdoing. But on Tuesday he buckled to pressure and said the inquiry should be handed to the Central Bureau of Investigation to avoid suspicion of political meddling.

The latest deaths included a national television journalist who began foaming at the mouth soon after interviewing the parents of Namrata Damor, a student who had obtained a college seat as part of the scam and was herself later found dead on train tracks in January 2012. The journalist died in hospital.

In the past few days, a policeman was found hanging from a ceiling fan, a trainee policewoman was found dead in a pond, and the dean of a college involved in the scam was found dead, with a half empty liquor bottle in a hotel room.

Chouhan denies accusations made by the opposition Congress party that he and other officials benefited from the fraud.

"There are very powerful big people involved in this," said the Congress party's Digvijaya Singh, a former Madhya Pradesh chief minister who wants the case be investigated by federal agents monitored by the Supreme Court.

On Tuesday, the Supreme Court said it would consider his petition along with several other relating to the case, at a hearing on July 9.

The scandal broke just as Indian media was lowering the pressure on the government over help given by the foreign minister and another regional leader to a controversial cricket-tycoon who fled a corruption probe and lives in London.

(Writing by Frank Jack Daniel; Editing by Jeremy Laurence)

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