* Senior member of hard-line nationalist Right Sector
* Movement played prominent role in president's ouster
* Under investigation in Russia for fighting in Chechnya
By Matt Robinson
KIEV, March 25 (Reuters) - A prominent Ukrainian far-right activist, part of a hard-line nationalist movement that played a leading role in the overthrow of President Viktor Yanukovich, was shot dead by police overnight, authorities said on Tuesday.
The Interior Ministry said Oleksander Muzychko, also known as Sashko Bily, was killed by officers of the 'Sokol' special unit as he tried to escape from a cafe in the western Ukrainian region of Rivne.
"At the moment of arrest, at shouts of "Stop! Police!", Muzychko fled, jumping through a window, and opened fire", first deputy Interior Minister Volodymyr Yevdokimov told a news conference in Kiev. The officers returned fire, killing Muzychko, he said.
Muzychko was a member of the hard-line Right Sector and the group's coordinator for western Ukraine, the country's nationalist heartland bordering the European Union. Police said he was wanted for "hooliganism" and an attack on a local prosecutor.
Russia - which cited the likes of Right Sector as justification for its move to annex Crimea and protect the peninsula's ethnic Russian majority from Ukrainian "fascists" - said this month Muzychko was under investigation for fighting alongside rebels in Russia's Chechnya region in the 1990s.
Contradicting the police account, independent lawmaker Oleksander Doniy said on his Facebook page that Muzychko had been executed. Muzychko had previously said he feared being killed by police.
"Two vehicles cut off his car. He was dragged out and put in one of them. Then he was thrown on the ground, hands cuffed behind his back, two shots to the heart," wrote Doniy, without saying where he got his information.
Yanukovich triggered peaceful street protests in late November by making a U-turn away from the European Union and towards closer ties with Russia. Right Sector raised the protests to a new level in January by attacking police vehicles with petrol bombs and bricks. It provided much of the muscle as clashes with police grew more serious.
Yanukovich fled after two days of gun battles in February between police and protesters, in which 95 people were killed.
Right Sector leader Dmytro Yarosh says he plans to run for president in a May 25 election, but is a rank outsider. (Additional reporting by Pavel Polityuk; Writing by Matt Robinson; Editing by Larry King)