Accrued sick time will carry over to the new year. However, if you are maxed out on your sick time, you will not earn anymore untill you use some of it. So says a friend of mine in New Jersey.
It will roll over. But you max out at 80. So you will not accrue any more until you spend some of that 80. Also here in CA, you can only use 48 sick hours a year. So in January people start taking extra days off to get under 80 and start accruing again. This may vary by state.