Whereas the federal government put blind and disabled children into a separate pool of enrollees for which states could seek funds, the state also included such children in its baseline for child enrollees. According to the audit, that is tantamount to duping the federal government.

Predictably, the state contests the findings of the audit. They did not seek to mislead the federal government, state officials contend, but were simply filling out federal forms that were designed in a contradictory and confusing way. Essentially, the problem is the feds' making, the state says.

Related: Newly covered cheer Medicaid expansion

The bonuses come from a 2009 law — the Children's Health Insurance Program Reauthorization Act — that set aside $3 billion in bonuses for states that hit certain benchmarks for enrolling children in Medicaid.

CHIPRA was in many ways the predecessor to the Medicaid expansion authorized by the Affordable Care Act the following year. Just like the ACA Medicaid expansion, it sought to incentivize states to boost Medicaid enrollment with the promise of additional federal money.

Most of the $157 million Colorado got from the law was legitimate, the audit found.

It's not only Colorado that is accused of scamming Uncle Sam, however. Alabama, New Mexico, North Carolina and Louisiana have also been hit with unflattering audits that accuse the states of inflating their Medicaid figures.

Related: Major insurers making money on Medicaid

While Colorado and New Mexico participated in the Medicaid expansion, Alabama, North Carolina and Louisiana, which were under GOP control, rejected the offer of additional federal funds to open up their public health programs to all those with incomes up to 133 percent of the federal poverty level. A newly elected Democratic governor in Louisiana reversed the state's position last year.