MOSCOW—A lawyer representing the family of dead Russian whistleblower Sergei Magnitsky was in intensive care after a fall from a four-story building ahead of a key court appearance, Mr. Magnitsky’s former employer said.

The lawyer, Nikolai Gorokhov, 53 years old, was due to appear in court Wednesday to argue that new evidence was grounds to reopen the case examining the demise of Mr. Magnitsky, who was found dead in prison in 2009 with broken fingers and bruises all over his body.

Russian state media said Mr. Gorokhov fell out of the building window late Tuesday, together with the bathtub he was helping workers carry to his apartment.

Campaigning group Justice for Sergei Magnitsky cast doubt on this version of events. The organization is run by Bill Browder, the owner of Hermitage Capital Management, which Mr. Magnitsky once represented.

“Russian state-controlled media contradict the information available from eyewitnesses,” the group said in a statement, adding that accounts differed over the whereabouts of various people at the scene of the alleged accident.