No. The exemption is based on customer ID (or PAN), so for all the braches of any bank, for all the FDs made during one financial year, it (form 15G/H) correlates.
DEAR SIR, ,,,,,,,,,,,,, BANK DID NOT DEDUCTION TDS IF INTEREST OF FD IS LESS THAN 10 THOUSAND AND YOUR PAN IS UPDATED ..............SO YOU NEED NOT SUBMIT FORM 15G/H , ONLY SUMBIT YOUR PAN NO.