The Soviet Union was called by the CIA (Central Intelligence Agency) once on a mission to develop telepathy. There were three CIA documents spanning the years 1963-1964 that were finally published by Government Attic, a transparency website that publishes declassified government documents.
The most interesting document shows a conversation between a CIA agent and Professor DA Kerimov of Leningrad University about the Soviet Union's 'cybernetics research' and 'extra-sensory perception'. They chatted over casual drinks and discussed the latest breakthroughs in Soviet mind control technology.
Professor Kerimov explained that he had heard scientists in Kyiv were working on a project that managed to tap the brain activity of a skilled musician while they were playing the piano. This brain activity somehow can then be recorded and played back to a non-musician. This method allows the person to play the piano with perfect mastery.
Surprisingly, Soviet scientists refused to go into detail about the research and CIA agents noted that some of these stories were quite dubious. Even so, Professor Kerimov said they have evidence that some people are able to pick up brain waves from others and even use this ability to predict random events in the future.
Kerimov admits that these ideas weren't taken too seriously in the past, but they're slowly starting to take an interest in them.
Lastly, CIA agents finish the report by noting that there is not much solid evidence. He noted that the Soviet Union's exploration into extra-sensory perception did not appear to be a national security threat.
"When I asked him what real developments had taken place as a result of cybernetics, he wasn't really ready to set an example," the agent wrote.
"I would say that there is not a single point, except for a fairly dubious story about wiretapping," he said.