Hey BLAT.

Yes, CLAT and BLAT both the law entrance exams are scheduled to be conducted on the same date ie.12th May. Usually in situations like this the schedule is changed. As CLAT is sought after more than BLAT there are chances that BLAT changes the schedule. But no official announcement regarding the same has been done. You can email the BLAT authorities with your grievances hoping that it is changes. Otherwise you'll have to attempt  only one.

But there are quite fair chances that BLAT will change it's date. As the same clashing dates with CLAT happened in 2017 after which BLAT had rescheduled their test. So you can expect but can't be sure.

Best of luck