State and local tax revenues grew during the last three months of 2010, continuing a recovery from the steep drops that followed the recession, the Census Bureau reported Tuesday.

Despite the modest revenue growth, state and local governments are contending with huge budget gaps that have led to service cuts and reductions in pay and rights for public employees.

Overall state and local tax revenue increased 1.6 percent to $378.3 billion during the fourth quarter of 2010 over the same time period in 2009, the Census Bureau reported.

The gains were led by a sharp increase in personal income tax receipts, and gains in sales tax receipts, gasoline taxes and revenue from liquor and tobacco taxes.

Corporate income tax was up 14.3 percent, after declining in nine of the previous 12 quarters, the bureau said. State corporate tax revenue was $10.3 billion in the final quarter of 2010, up from $9 billion a year earlier.

States also saw a boost from “severance,” or taxes paid for extracting coal, oil or other natural resources, which were up 11.5 percent to $2.9 billion from the last three months of 2009.

Though the recovery in state revenues is good news for state and local governments, it has not been sufficient to compensate for the huge revenue losses caused by the recession. States also are coping with fast-increasing costs for Medicaid and higher education, while they are bracing for the loss of about $50 billion in federal stimulus money in the coming budget year.

In addition, states face huge long-term costs in funding pension and health-care obligations that — in the most extreme cases — are beginning to crowd out money for core government services.

“Although state tax revenue is recovering, it is a little like falling off a cliff and climbing halfway back up,” said Donald J. Boyd, senior fellow at the Rockefeller Institute of Government. “You’re a long way from the bottom. But you are also a long way from the top.”

Property tax revenue, the backbone of local government financing, was down 2.9 percent to $177 billion in the fourth quarter of 2010 from a year earlier, the Census Bureau reported.

The decline in property tax revenue comes as many cash-strapped states are making deep cuts in aid to local governments and education to close their budget gaps, putting additional pressure on local budgets.

“While the economy is clearly recovering, state governments still have a ways to go and local governments do as well,” Boyd said.