In what month do the dept. of labor sends out your w2 forms

We don't know, what is this for, unemployment, Often they don't send out W2 but you log into your account and print if online.

But only the agency that is suppose to send it, will know,

The unemployment form is 1099-G, and it should be mailed by the end of the month.

You might want to check out the state Department of Labor website. The 1099-Gs are often available there.