Terming the practice as "atrocious", he said it gives an impression that the whole district was directly or indirectly guilty of actively supporting and harbouring terrorists.
He was speaking at the Chief Ministers conference here in which he strongly opposed the proposed National Counter Terrorism Centre (NCTC) demanding its "immediate withdrawal".
Kumar questioned the method of investigation adopted by central investigative agencies and the police in some recent cases in which the accused were arrested from North Bihar.
"Recently, there have been instances of central agencies and the police of some other states making few terror-related arrests of original residents of some districts in Bihar. In media, such events were reported as busting of terror modules identified as Darbhanga module or Madhubani module," he pointed out.
Suggesting that such a practice could fan a sense of alienation among a particular community, the Bihar Chief Minister said "Should we not try to isolate those two or three persons suspected to be terrorists from the total population of 20 to 30 lakh residing in the district?"
"Is it proper to let the whole district be branded as a terrorist hub? Will this not lead to widespread sense of resentment and alienation among residents of the district?"
He added that the the practice of calling "tiny groups of accused" after the name of a district should be stopped forthwith.