* Russian stocks slump to mid-August lows

* Rouble slides lower against dollar, euro

* Moscow rekindles martial law fears with legislation

* Russia plans territorial referendums in east Ukraine

* This content was produced in Russia where the law restricts coverage of Russian military operations in Ukraine (Updates prices, adds bullets)

By Alexander Marrow and Felix Light

MOSCOW, Sept 20 (Reuters) - Russian stocks plunged to their lowest in a month on Tuesday as Moscow reignited martial law fears with new legislation and plans to hold referendums on Russian-controlled regions in east Ukraine sped forwards apace.

Stocks hit their lowest since mid-August, with the dollar-denominated RTS index down 9.2% to 1,155.1 points as of 1542 GMT. The rouble-based MOEX Russian index was 8.7% lower at 2,218.0 points, earlier sinking to 2,171.92 points, its lowest point since Aug. 16.

Russia's parliament on Tuesday approved a bill to toughen punishments for a host of crimes such as desertion, damage to military property and insubordination if they were committed during military mobilisation or combat situations.

"Indices are clearly collapsing amid fears around the risks of mobilisation and martial law," said Tinkoff Investments analyst Kirill Komarov, adding that Tuesday's collapse would likely be the MOEX index's sharpest drop since June 30.

"They are fuelled by news of imminent referendums... as well as the president's order to boost defence output."

Russian-installed leaders in occupied areas of four Ukrainian regions set out plans for referendums on joining Russia this week, a step an ally of President Vladimir Putin said would alter the geopolitical landscape forever.

"The sell-off was triggered by the relevance of the geopolitical factor," said BCS Express in a note. "In addition, there are media reports about the government planning to introduce an additional tax on exporters of oil, gas and LNG from 2023."

Energy companies dominate Russia's blue-chip index.

ROUBLE SLIDES

The rouble, too, slid lower, moving away from the 60-mark against the dollar and euro. Against the dollar, the rouble was down 0.6% at 60.50, and had lost 0.6% to 60.49 versus the euro.

The Russian currency is set to gain support from a month-end tax period that usually sees Russia's exporters convert their foreign currency earnings into roubles to pay to the treasury, the peak of which falls on Sept. 26.

"We note that the dynamics of trading, according to our estimates, despite the beginning of the key week before the payment of taxes by exporters, may partly be associated with a shortage of foreign exchange liquidity for a number of players,"

said Promsvyazbank analyst Egor Zhilnikov.

Zhilnikov said that after the Russian central bank's 50-basis point rate cut last week to 7.5%, the dollar overnight basis became negative, "which means that the exchange of dollars for roubles began to cost banks more than direct loans in roubles".

The rouble has been the world's best-performing currency this year, buoyed by emergency capital controls rolled out by the central bank in a bid to halt a mass sell-off. (Reporting by Felix Light and Alexander Marrow; additional reporting by Darya Korsunskaya; Editing by Raissa Kasolowsky, Alex Richardson, Alexandra Hudson)