(Changes headline to reflect U.S. dollar's decline)

* Republican healthcare bill collapses in Senate

* Faith in Trump's ability to boost U.S. growth wavers

* Euro, Swiss franc touch more than 1-year high vs dollar

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

By Sam Forgione

NEW YORK, July 18 (Reuters) - The dollar hit its lowest against the euro and Swiss franc in more than a year on Tuesday, with the broader dollar index touching a more than 10-month low, on reduced confidence in U.S. President Donald Trump's agenda and jitters over hawkish central banks abroad.

Republican senators' effort to pass their own healthcare overhaul bill collapsed late on Monday, stoking doubts over the likelihood that Trump's pro-growth agenda would come to fruition.

Traders also remained doubtful the Federal Reserve would be able to raise interest rates again this year, while other central banks including the European Central Bank and Bank of England have signaled a more hawkish bent toward tightening policy.

"The setback for Trump is a setback for the U.S. dollar," said Kathy Lien, managing director at BK Asset Management in New York. "Based upon the failed repeal of Obamacare, I think that really casts doubt on the Trump administration's broader strategies."

The euro touched $1.1583 against the dollar, its strongest since early May 2016, with analysts noting traders who had "shorted" or bet against the euro were being forced to "cover" or repurchase the currency.

The dollar index, which measures the greenback against a basket of six major rivals, touched its lowest since early September of 94.476. The dollar touched 0.9525 franc , its lowest against the Swiss currency since late June 2016, while the dollar hit a three-week low against the Japanese yen of 111.69 yen.

The dollar index has fallen 7.5 percent since the start of the year, partly on the doubts over Trump's fiscal stimulus agenda, with much of the downdraft starting in early March. The Australian dollar was a beneficiary of the greenback's weakness on Tuesday and surged to a more than two-year high of $0.7942 .

"This is a tremendous short squeeze in the euro on the break of $1.15, and that has resulted in a significant rally as shorts bail out of their positions," said Douglas Borthwick, managing director at Chapdelaine Foreign Exchange in New York.

Friday's weak reading on U.S. inflation and retail sales fanned speculation the Fed may not have justification for another rate hike by the end of this year, despite policymakers' projection for such a move. (Reporting by Sam Forgione; Additional reporting by Patrick Graham in London; Editing by Chris Reese)