By Thomas Grove

MOSCOW (Reuters) - Russian investigators have dropped an investigation into the death in custody of a whistleblowing anti-corruption lawyer, prompting his allies and human rights campaigners to accuse the Kremlin of a cover-up.

The Investigative Committee, a government agency, said on Tuesday it had found no evidence that a crime was committed when Sergei Magnitsky died at the age of 37 while awaiting trial in 2009 on charges of tax evasion and fraud.

The Kremlin's own human rights council said in 2011 that Magnitsky, who had accused state officials of stealing $230 million in a tax fraud, was probably beaten to death.

President Vladimir Putin has said Magnitsky was not tortured and that he died of heart failure.

"In the course of the investigation of the criminal case, no objective facts have been established regarding a crime in relation to Sergei Magnitsky," the Investigative Committee said in a statement. "A decision has been taken to end the criminal case because of the absence of a crime."

It announced the decision three days before the posthumous trial of Magnitsky is due to start in Moscow, the first time Russia has put a dead man in the dock.

The case has aggravated tension in relations between the United States and Russia and intensified criticism of a lack of independence in Russia's judiciary, although the Kremlin says it does not interfere in legal cases.

"STATE COVER-UP"

The Hermitage Capital Management fund, for which Magnitsky had been working, says the lawyer was beaten to death and had been refused treatment while in pre-trial detention.

It issued a statement accusing the Russian authorities of trying to protect the officials he had accused of embezzlement.

"Closing the criminal case into Sergei Magnitsky's death over lack of evidence is proof that the Russian state has officially taken a position in defense of the torturers and killers of Sergei Magnitsky," it said.

Putin's spokesman, Dmitry Peskov, declined comment on the statement.

No one has been held accountable for Magnitsky's death. A prison official was tried last year but prosecutors abruptly asked the court to clear him shortly after Putin said Magnitsky had not been tortured, and the judge complied.

"This was to be expected. I don't believe that it is possible today to obtain the truth in Russia since somebody has an interest in concealing it and somebody is controlling this case," Hermitage quoted Magnitsky's mother, Natalya, as saying.

The case against Magnitsky is seen by human rights groups as a test of the independence of the Russian judiciary. Such groups say the posthumous trial is politically motivated and intended by the Kremlin to discredit Magnitsky's accusations.

"Lawlessness - what else can I say of it?" said a leading human rights activist, Lyubov Volkova.

The United States passed legislation late last year to introduce a visa ban and assets freeze on officials involved in the Magnitsky case, as well as other Russians whom Washington says have violated human rights.

Moscow responded with similar moves to punish Americans accused of violating human rights and barred U.S. couples from adopting Russian children.

Kremlin critics have accused Putin of clamping down on opponents since his return to the presidency last May, saying he has used the threat of legal action against some of his leading opponents to smother dissent following the biggest protests since he first rose to power in 2000. Peskov has denied this.

(Additional reporting by Maria Tsvetkova and Gabriela Baczynska, Editing by Timothy Heritage and Mark Heinrich)