By Elaine Lies and Ami Miyazaki

TOKYO (Reuters) - Voters in the Japanese capital head to the polls on Sunday and could elect their first woman governor, after two predecessors stepped down over scandals that clouded the city's preparations to host the 2020 summer Olympic Games.

Opinion polls show that Yuriko Koike, Japan's first female defense minister, leads former bureaucrat Hiroya Masuda and liberal journalist Shuntaro Torigoe.

Koike, 64, is a member of Prime Minister Shinzo Abe's ruling Liberal Democratic Party (LDP) but angered the party's Tokyo branch by not getting its approval before announcing her candidacy for city governor.

The LDP instead drafted Masuda, 64, who once served as governor of a rural prefecture.

"I often reflect that I'm terrible at traditional Japanese skills like consensus-building, but my passion was stronger," Koike told a news conference this month.

According to polls published last weekend, Masuda was in second place while Torigoe, a 76-year-old cancer survivor who is backed by several opposition parties, trails both. But about 30 percent of voters were undecided.

The sprawling city of some 13.5 million people faces a plethora of problems such as an aging population, daycare shortage, and the ever-present possibility of a big earthquake.

But a big issue in the campaign has been the 2020 Olympics, which Japan hopes will spur its economy, struggling to escape decades of deflation.

There has been a string of problems since the city won the games in 2013.

Construction of the main stadium has been delayed and the original logo for the games had to be scrapped after plagiarism accusations.

After the resignations of the city's two previous governors, the new one will be responsible for saving Tokyo's reputation as host for the games.

One of the governor's first duties will be to travel to Rio de Janeiro when the curtain comes down on next month's games there to accept the Olympic flag as the next host.

"The Olympics are right in front of us. I want to use them as a chance to build a new Tokyo for beyond 2020," Koike said when the campaign began.

Though the LDP and its coalition partner back Masuda, fallout for Abe will likely be minimal if he does not win.

"This is basically a Tokyo issue," said Kenji Yumoto, vice chairman of the Japan Research Institute think-tank.

"Abe's prestige probably won't be damaged and support for the LDP won't fall."

(Reporting by Elaine Lies; Editing by Linda Sieg, Robert Birsel)