Chancellor challenged over use of taxpayers' money to keep Nissan in Sunderland
The chairman of the influential House of Commons Treasury Committee, Andrew Tyrie, has written to the Chancellor to ask for "clarity" over the deal.
Nissan announced in October it was extending production of Qashqai and X-Trail models in the North-East, securing 7,000 jobs.
Ministers have strongly denied suggestions they offered the firm a "sweetheart deal", but have refused to publish a letter of reassurance sent to Nissan boss Carlos Ghosn.
In his letter, Mr Tyrie demanded to know whether the Treasury had been asked for - and supplied - its consent to an offer of financial or other assistance to Nissan or the automotive sector as a whole to compensate for the possible negative impact of withdrawal from the European Union.
He asked whether the assurances involved any commitment to the potential future use of public funds, which Treasury rules say should be reported to Parliament.
And he asked whether Prime Minister Theresa May or any of ministers and officials had consulted the Treasury about whether the support offered to Nissan was compatible with state aid rules and the requirements of the World Trade Organisation.
Mr Tyrie said: "The Government has not yet clarified whether any form financial assistance has been discussed with Nissan to persuade it to stay in Sunderland.
"If it has made commitments that could lead to a call on public funds, the Government would have a duty to inform Parliament about them now. So I have written to the Chancellor to ask for clarification.
"The position taken by the Chancellor before the Treasury Committee that `we are not going to give a running commentary on how we will conduct the negotiation and what our priorities will be within it' sits oddly with the commitments - on tariffs and protection from bureaucracy - apparently made by the Business Secretary, first in private to Nissan, then later to the BBC, and, later still, to the House of Commons.
"A running commentary for a few firms, but not the rest of UK business, would be both unacceptable and counter-productive."