Do I have a legal right to sue my former employer for trying to get out of paying unemployment benefits?

The company I worked for down sized and did away with my job at the end of July. I received a severance package and I can start drawing unemployment, except when I filed my claim with the unemployment office my former employer told them that I was stilled employed. They now owe me almost 4 week of unemployment pay. The unemployment office said it could take as long as 10 weeks to resolve this. Do I have a legal case to sue my former employer.