PHOENIX — Arizona’s seasonally adjusted jobless rate dropped slightly last month. But it’s not because more people are working.

 In fact, the reverse is true: New figures from the state Department of Commerce show the number of people employed in Arizona declined by 4,600 from March.

 The reason the unemployment rate declined is that the number of Arizonans actually out looking for work declined even more, by 12,500. The one thing state officials don’t know is whether that’s because discouraged jobseekers have simply given up looking and are sitting at home, or whether they’re actually leaving the state.

 By the numbers, the state’s jobless rate in April was 3.9 percent, down a tenth of a point. Identical 0.1 point declines were registered for the Phoenix metro area, to 3.4 percent, and for the Tucson area at 3.8 percent.

 But that was counterbalanced by that 4,600 drop in workers. Once again, the construction industry remained the weakest spot in the economy, losing another 3,200 jobs in April.

Dennis Doby, senior director of research administration at the Department of Commerce, said the only bit of good news about that figure is it is less than the 3,700 job loss posted in March. But construction employment last month still is 26,100 below a year earlier.

 That soft housing market also continues to have ripple effects elsewhere, notably in the state’s finance sector.

There, 600 people lost their jobs in April, with a year-over-year loss of 7,900.

 But employment by stores that sell building materials and garden equipment actually showed some signs of life, picking up 100 new workers. That, however, is still 1,900 below a year earlier. Arizona’s jobless rate still remains below the national average of 5.0 percent, which also is down a tenth of a point from March. But Doby said that is not anything to cheer about. ``The fact that the unemployment rate is 3.9 percent is not necessarily indiciative of a good economy,’’ he said, because of the number of jobs that continue to be lost even as others stop looking for work.

 Doby also said his agency has no way of knowing whether the decline in the number of people employed or even actively seeking work is related to the state’s new employer sanctions law.

 That statute, which took effect in January, allows a judge to suspend or revoke any business licenses of firms found guilty of knowingly hiring undocumented workers.

There has been some anecdotal evidence of companies combing their payroll records and letting workers go after these employees were unable to prove legal residence.

 So when does state hit bottom? ``I hope soon,’’ he said, citing the slower decline in construction employment in April compared to March. But Doby said he cannot predict whether employment numbers will actually start rising later this year or early next year.