The city's unemployment rate last month stayed steady at 9.1%, the same as January and down from 9.4% in February of 2012, according to new figures released Thursday from the state Labor Department. New York state's unemployment rate remained at 8.4%, where it was in January, about 0.7% higher than the national rate. In New York City, the private sector job count rose by 700, not seasonally adjusted, between January and February. A gain of close to 17,000 is typical during that period. The financial sector shed 3,200 jobs when it usually stays flat. The hospitality industry, which usually posts a gain of about 3,200 in that time frame, added only 700 jobs. The health and education sectors, meanwhile, added less than half the number of jobs that is considered normal: 5,900 instead of 12,000 in February.