U.S. crude falls to end below $40/bbl for first time since April

* Short-covering, weak dollar helps oil recover

* Nagging glut worries, lower U.S (Other OTC: UBGXF - news) . equities mitigate rebound

* API (Stuttgart: 565969.SG - news) reports 1.34 mln bbls crude draw, within expectations

* Coming up: U.S. government crude inventory data, Wednesday (Adds API data and market reaction in post-settlement trade)

By Barani Krishnan

NEW YORK, Aug 2 (Reuters) - U.S. crude oil fell on Tuesday to end below $40 a barrel for the first time since April as persistent worries of both a crude and refined fuel glut and a slide in U.S. equities offset an early boost from a weak dollar.

"There is much talk about the product glut replacing the oil glut, and this is a worrisome indicator for crude demand," said Frank Klumpp, oil analyst at Stuttgart-based Landesbank Baden-Wuerttemberg.

U.S. West Texas Intermediate (WTI) crude settled down 55 cents, or 1.4 percent, at $39.51 a barrel, after earlier rallying to $40.91. On Monday, it slid to an intraday session low below $40 for the first time since April.

Brent crude fell 34 cents, or 0.8 percent, to settle at $41.80, after touching a session high at $43.18.

Both WTI and Brent held losses in post-settlement trade after preliminary inventory data from trade group American Petroleum Institute (API) showed that U.S. crude stockpiles fell 1.34 million barrels last week, largely within expectations. The U.S. government will issue official inventory data on Wednesday.

Early in the session, oil rallied, helped by the dollar's drop to a six-week low. U.S. stocks later tumbled to a three-week bottom, mitigating the support lent by the weaker dollar.

"I am bullish here overall but worry about being too early," said Scott Shelton, energy futures broker at ICAP (Frankfurt: A0BKYB - news) in Durham, North Carolina. "I also wonder if the market is going to chop around a bit first, like it did in late May to June before dropping after many threw in the towel."

Oil hit 2016 highs above $50 a barrel between late May and June as crude supplies tightened from disruptions in Canada, Nigeria and Libya, and a near economic meltdown in OPEC member Venezuela. The rally faded soon after as higher prices spurred more output of crude and refined products.

Global fuel stockpiles are brimming. Refineries have churned out huge volumes of diesel, gasoline and jet fuel. Crude remains oversupplied as top OPEC oil producers pump near record high levels.

Saudi Arabia has cut its crude selling price to Asian customers, signaling another price war and tussle for market share.

Hedge funds and other speculators have turned more bearish toward crude and refined products in the last two months amid signs of a gasoline glut.

"With (Other OTC: WWTH - news) the market continuously focussing on oversupply, this bearish trend seems hard to change in the near term," said Hans van Cleef, ABN AMRO senior energy economist. (Additional reporting by Karolin Schaps in LONDON and Henning Gloystein in SINGAPORE; Editing by Marguerita Choy)