Census officials and researchers have long expressed concerns about the old version of insurance questions in the Current Population Survey, and for more than a decade the agency has been trying to make it more accurate.

The questionnaire traditionally used by the Census Bureau provides an “inflated estimate of the uninsured” and is prone to “measurement errors,” said a working paper by statisticians and demographers at the agency.

In the test last year, the percentage of people without health insurance was 10.6 percent when interviewers used the new questionnaire, compared with 12.5 percent using the old version. Researchers said that they had found a similar pattern in the data for different age, race and ethnic groups.

In addition, “the percentage of people with private coverage was statistically higher” when the bureau tested the new questionnaire, the working paper said. For reasons that are not clear, people were less likely to respond when interviewers used the new questionnaire.

Another Census Bureau paper said “it is coincidental and unfortunate timing” that the survey was overhauled just before major provisions of the health care law took effect. “Ideally,” it said, “the redesign would have had at least a few years to gather base line and trend data.”

The old questionnaire asked consumers if they had various types of coverage at any time in the prior year. The new survey asks if they have insurance at the time of the interview — in February, March or April — then uses follow-up questions to find out when that coverage began and what months it was in effect. Using this technique, census officials believe they will be able to reconstruct the history of coverage month by month over a period of about 15 months.

However, Mr. O’Hara of the Census Bureau said the agency was not planning to release coverage data from early this year in its next report. Agency officials want to assess the reliability of the monthly data, being collected this year for the first time.