A Dec. 31 deadline for renewing enrollment for school tax relief, or STAR, is approaching fast. Those who do not register with the state by that date could lose their share of the 2014 break. Even those who have previously been in the STAR program have to sign up; state tax officials hope the process will check for income levels and help weed out cheats, such as those with double exemptions. Eligibility requirements are that a house be a primary residence and owner-occupied, and that household income be less than $500,000.