* Aussie slides half a pct after RBA
* Euro hits more than three-week low as dollar gains
* Sterling under pressure again on Brexit vote woes
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh
By Tommy Wilkes
LONDON, April 2 (Reuters) - Australia's dollar shed half a percent on Tuesday as investors focused on the central bank's caution about the health of the global economy. The U.S. dollar rose to a three-week high.
The Reserve Bank of Australia has left interest rates unchanged and avoided the outright dovish tone of some other central banks, but traders still treated its policy statement as bad for the currency.
The RBA's stress on the "downside risks for the global growth environment" probably caused the currency to weaken, said Commerzbank analyst Esther Reichelt.
She said the government's budget due on Tuesday should provide some supportive measures. Combined with optimism over China, she said, that should help the Aussie to rebound.
Australia's dollar dropped 0.6 percent to $0.7072.
The euro, which has also been weakened by a dovish central bank, fell 0.2 percent to $1.1196 in London on Tuesday -- its weakest since March 8 -- as the U.S. dollar gained.
The dollar index, which measures the U.S. currency against a basket of rival currencies, rose 0.3 percent to 97.430, a three-week high.
Sterling dropped half a percent after lawmakers rejected four Brexit proposals, heightening Britain's uncertainty just 10 days before it is due to leave the European Union. The pound was down at $1.3044 and at 85.84 pence against the euro .
The safe-haven Swiss franc held below 1.12 per euro and near 2019 highs. It traded 0.1 percent higher at 1.1186, below 2019 highs of 1.117.
RBC Capital Markets strategist Adam Cole said he did not expect the franc to hold its gains because the Swiss National Bank remained "sensitive" to a stronger currency, particularly when it traded below 1.12 francs versus the euro.
The SNB will be "the last central bank in the developed world to tighten rates," he said.
Cryptocurrencies surged. Bitcoin jumped 20 percent to touch $5,000, its highest since November. (Additional reporting by Shinichi Saoshiro in Tokyo, editing by Larry King)