Some of those measures were passed by decree, but others need to go through the legislature.
The clash broke out when the estimated 300 demonstrators, most of them civil servants, tried to overrun the state assembly in downtown Rio.
They were dispersed by police. Streets were blocked off and traffic was diverted.
Some within the group hurled projectiles at police and the assembly building. Police fought back with the percussion grenades, rubber bullets and tear gas.
The newspaper Folha de Sao Paulo said at least two people were hurt by rubber bullets.
Last month governor Luis Fernando Pezao presented a package of unpopular spending cuts and tax increases to try to fix heavily indebted Rio state's financial woes -- just one sad chapter of the overall national economic crisis and recession. Just months ago the city of Rio hosted the Summer Olympics.
Some of those measures were passed by decree, but others need to go through the legislature. The voting began Tuesday and is scheduled to last through next Monday.
State officials forecast for this year a deficit equivalent to 5.4 billion dollars. Without the austerity measures, they say, the shortfall would balloon to three times that by the end of 2018.
The package calls for a cut in spending on social programs, an increase in what workers pay into the state pension system, a rise in public transport fares and reductions in retirement pensions.
The economic crisis has wreaked havoc in health care and public safety, and the city has endured an alarming rise in the crime rate.