The unemployment rate in Texas, the nation's leading energy-producing state, rose to 8.4 percent in February -- an unprecedented two-percentage-point jump from the previous month that Democratic Gov. Mark White called "the first casualty report from the energy battlefront."

The price of oil in Texas has fallen from $25 a barrel late last year to as low as $12 a barrel this month, creating severe financial problems in the industry and the entire state economy.

Although the statistics released today did not analyze the figures by industry or regions of the state, labor economists said the largest share of the newly unemployed came from the energy industry, which is concentrated in the Houston area and in the Permian Basin of west Texas.

Terence Travland, research economist for the Texas Employment Commission, said he believes that the February figures, based on the Texas portion of a national household sample, were a slight overstatement of the jobless situation in the state.

"I don't think it's really that bleak," Travland said.

"It is quite serious, no doubt, but not disastrous. It certainly reflects the precipitous drop in oil prices, plus the stagnancy of agriculture, the semiconductor industry and real estate," he said.

Since the Depression, the jobless rate in Texas never has reached double digits. The highest rate was during the recession of February and March 1983, reaching 8.5 percent and 8.6 percent.

The 8.4 percent figure in February represented 671,000 persons without jobs, up from 510,000 in January.

The poorest section of Texas, the Rio Grande Valley near the Mexican border, has had unemployment rates of 15 to 20 percent in recent years, attributable to peso devaluations, which have hurt tourism, and to freezes, which have hurt the citrus industry.

But economic conditions in the Valley have been improving slightly in recent months. Houston is predicted to be the next area where the unemployment rate surpasses 10 percent.

Harold Gross, an economist at Southern Methodist University who specializes in the oil industry, said employers in Dallas and Houston were starting to let people go and enact hiring freezes "in response to the prospect of oil prices in the low teens for the next six to nine months."

White, whose state government is facing a $1.3 billion budget shortfall largely because of declining oil revenues, again called on President Reagan to impose a tariff on imported oil, an idea that Reagan has rejected several times, most recently last week.

"If the federal government does not take immediate action to protect a domestic energy industry so essential to our national security interest, then the list of economic casualties can only grow as more and more Americans find themselves out of work," White said.