DUBAI, May 9 (Reuters) - The Iranian rial plunged to a record low against the U.S. dollar in the free market on Wednesday after U.S. President Donald Trump decided to withdraw from a deal on Tehran’s nuclear programme, fuelling fears of an economic crisis in Iran.

The dollar was being offered for as much as 75,000 rials, compared to around 65,000 just before Trump announced his decision on Tuesday night, according to foreign exchange website Bonbast.com (www.bonbast.com), which tracks the free market.

Dealers in Tehran quoted similar levels on Wednesday, according to an Iranian economist outside the country who is in touch with them. One dealer said the rial had hit 78,000, while another said he had made two sales of dollars at 80,000.

The currency has been sliding for months because of a weak economy, financial difficulties at local banks and heavy demand for dollars among Iranians who feared a pullout by Washington from the nuclear deal, and renewed U.S. sanctions against Tehran, could shrink the country’s exports of oil and other goods.

The rial has tumbled from around 57,500 at the end of last month and 42,890 at the end of last year -- a freefall that threatens to boost inflation, hurt living standards and reduce the ability of Iranians to travel abroad.

In an effort to halt the slide, Iranian authorities announced last month they were unifying official and free-market exchange rates at a single level of 42,000, and banning any trade at other rates under the threat of arrest.

But this step failed to stamp out the free market because authorities have been supplying much less hard currency through official channels than consumers are demanding. Free market trade simply went underground, dealers said.

Tehran residents told Reuters on Wednesday that activity in the free market had decreased considerably, because people feared getting arrested and the wild volatility of exchange rates increased the risk for dealers.

Nevertheless, the dealer who reported dollar sales at 80,000 said one of his sales was to a person who had sold his apartment a week ago. This person had now decided to buy dollars instead of another apartment in Iran, he said. (Reporting by Andrew Torchia; Editing by Toby Chopra)