I used turbo tax to process state and federal return. The co form shows -350 on line 1, the federal form shows 0. Is the state correct with this number?

The federal return does not allow a negative number -- it is limited to zero.  Under Colorado rules, if the federal taxable income is calculated as a negative number, it is entered as a negative number for Colorado.  It isn't limited to zero for CO line 1 purposes.