The landmark 2006 Massachusetts health-care law that inspired the federal overhaul didn’t lead to a reduction in unnecessary and costly hospitalizations, and it didn’t make the health-care system more fair for minority groups, according to a new study that may hold warnings for the Affordable Care Act.

Massachusetts’ uninsured rate was cut by half to 6 percent in the years immediately following the health-care law signed by then-Gov. Mitt Romney. Blacks and Hispanics, who have a harder time accessing necessary medical care, experienced the largest gains in insurance coverage under the Massachusetts law, though they still were more likely to be uninsured than whites.

The new study, published in the BMJ policy journal, examined the rates of hospitalizations for 12 medical conditions that health-care researchers say wouldn’t normally require hospitalization if a patient has good access to primary care. These include hospitalizations for minor conditions like a urinary tract infection, or chronic conditions that would require repeat primary care visits over the course of a year.

“It’s thought to be a good measure and one of the few objective ways of looking at access [to health-care provider] in the community,” said Danny McCormick of Harvard Medical School, the study’s lead author.