In March, the office of TNK-BP was searched by Russian police.
The Kremlin has cranked up the pressure on BP's Russian oil venture after Moscow prosecutors questioned staff.
A district prosecutor asked TNK-BP for more documents after quizzing company representatives about whether the firm met Russian employment rules.
Relations between the firm, owned by BP and a group of Russian businessmen, and the government have been tense.
TNK-BP employees have faced accusations ranging from spying to tax evasion in recent months.
It is the latest challenge for the company's American chief executive Robert Dudley.
Russian shareholders have demanded a management shakeup at the firm and have accused Mr Dudley of working only in BP's interests.
This weekend he was forced to defend his leadership and the shareholding structure of the firm at an investor meeting.
He also defended TNK-BP's use of foreign executives seconded from BP, saying the policy benefitted Russia's oil and gas sector.
The company, 50% owned by BP, is reported to be considering a sale of half of the business.
State-run gas giant Gazprom is thought to be keen to buy the Russian-owned half, sparking controversy over the state-run group's growing dominance in the energy market.
TNK-BP's offices in Moscow were raided by security services and one of its employees was accused of industrial espionage.
Foreign staff have also faced problems with visa problems and there is an investigation into alleged tax evasion involving a former unit of TNK-BP.
Analysts have said the inquiries could be part of a state-backed campaign to force a sale to a Gazprom.
Last year, TNK-BP was forced to cede control of a Siberian gas project to Gazprom.