Last December the committee, made up of politicians from both houses of Parliament and all three main political parties, called for the inquiry in a report, Deaths in Custody, in order to learn from Scholes' death.
But the Government rejected the call on the grounds that the steps it has taken are adequate. It has asked the Sentencing Guidelines Council to look at the sentence, the Youth Justice Board to examine custody for juveniles, and David Lambert, a former assistant inspector at the Social Services Inspectorate, to investigate operational issues.
Deborah Coles, co-director of pressure group Inquest, said: "There is no cause for optimism."
The Government said it was still considering the committee's main recommendation of a cross-departmental body to look at the issue of deaths in custody.
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