The move could increase pressure on Weizman, a powerful figure in Israel, to resign. The president's role in Israel is ceremonial, but he wields significant influence.
At issue is $430,000 that Weizman allegedly received between 1988 and 1993, when he was a lawmaker and government minister.
At a hastily called evening news conference, Attorney General Elyakim Rubinstein stressed that the police inquiry was "not a criminal investigation."
State Attorney Edna Arbel explained that prosecutors themselves did not have the means to conduct the inquiry properly, and therefore needed to call in the police.
"In the 48 hours since we were given the material by the president's attorneys, we conducted a marathon of checks," she said. "We did not succeed... we don't have the tools to do this. Therefore, we decided that the matter will be transferred... to the police."
Weizman has resisted growing calls to resign, and has denied reports that he was negotiating a plea bargain deal.
Critics say that even if Weizman's actions were not strictly illegal, it was unethical for him to receive so much money while holding public office.
Prime Minister Ehud Barak on Wednesday offered Weizman only guarded support.
"I am sure that, depending on the results, he will know how to behave," Barak said.
Weizman has acknowledged accepting money from millionaire Edouard Sarousi but says the sum was less than alleged. He said he consulted his lawyer at the time and was told there was no need to report or pay taxes on the gift.
Weizman is the nephew of the country's first president, Chaim Weizmann and helped found and eventually commanded Israel's air force. He was an architect of Israel's lightning victory in the 1967 Mideast war, and was elected president in 1993.
His second five-year term expires in 2003.
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