* LME/ShFE arb - http://tmsnrt.rs/2oQ5nm2 (Recasts, updates prices, adds comment/detail; changes dateline)
LONDON, June 28 (Reuters) - Copper, lead and zinc prices slipped on Wednesday after hitting near three-month highs as a boost from a weaker dollar and signs of tighter supply gave way to worries over U.S. economic growth and falling oil prices.
U.S. stocks had one of their worst days of the year on Tuesday as President Donald Trump's healthcare bill was delayed, raising renewed doubts about his ability to push through other agenda items such as tax cuts and spending increases.
Oil prices fell on Wednesday on concerns that a three-year old crude glut is far from over. Weaker oil prices deter investors from commodity basket funds that include metals.
Still, metals have been underpinned recently by signs that supply is shrinking as exchange inventories fall and indications of solid demand in China, the world's largest metals consumer.
"As we head into summer, we expect more capacity reductions in China to meet environmental restrictions, and we think consumers are buying stock ahead of that," said SP Angel analyst John Meyer.
"The market got ahead of itself in the first quarter with (hopes for) Trump's infrastructure plans, that's not happening now but against that China growth is ok."
* COPPER PRICE: London Metal Exchange copper traded down 0.3 percent at $5,838.50 a tonne by 1013 GMT, having struck its highest since early April at $5,870.
* COPPER STOCKS: LME data showed headline copper stocks <MCU-STOCKS> down to 248,675 tonnes, having slid 30 percent since early May, and on-warrant or available stock levels have shed 40 percent over the period.
* LEAD & ZINC: Zinc fell 0.4 percent to $2,736, having hit its highest since early April at $2,764, while lead was flat at $2,286, having reached its strongest since early April at $2,299.50.
* TECHNICALS: Cash zinc traded at a premium of $0.25 a tonne to the three month price <CMZN0-3>, a high since early May and indicating tight nearby supply. Cash lead traded at a discount of just $13.25 to the three month price <CMPB0-3>, its narrowest since mid-May.
* CHINA POLLUTION: China on Tuesday appointed a new environment minister who has promised a "protracted battle" to clean up the nation's notoriously polluted air, water and soil.
* USD: The dollar hit a one-year low versus the euro after comments by European Central Bank President Mario Draghi convinced investors that he is ready to start withdrawing emergency stimulus measures.
A weak dollar makes dollar-priced metals cheaper for non-U.S. investors.
($1 = 6.7999 Chinese yuan renminbi)
(Additional reporting by Melanie Burton, editing by David Evans)