The law states your deadline to file an appeal is 30 days AFTER the date the notice was mailed, or May 15th, whichever is greater.
You should check with your individual appraisal district's website to confirm the deadline, but the below schedule is what we believe to be the deadlines to file a protest are in various counties.
Collin: June 15th (notices will be mailed May 15th)
Dallas: June 15th (notices will be mailed May 15th)
Denton: May 30th (notices will be mailed April 29th)
Harris: May 15th (notices were mailed March 31st)
Tarrant: June 1st (notices will be mailed on May 1st)
Pro tip: Go to google and type "30 days from [insert date]". If you enter the date the notice was mailed, be sure and and 1 day to it because it is 30 days AFTER the notice was mailed.