The police claimed the processions had to be stopped as they were being taken out without permission.
In Uttarpara, BJP workers scuffled with the police after their procession was obstructed soon after it began. Later, the BJP activists blocked the Grand Trunk Road.
State BJP general secretary Sayantan Bose warned that the police action would send a message across India that there is no democracy in the state.
"There is no need for informing or seeking permission from the police. The Chief Minister (Mamata Banerjee) is holding so many rallies and meetings. Is she taking permission from the police?" asked Bose.
He said the BJP would continue to take out processions as they were not protesting but only thanking the Prime Minister Narendra Modi for clearing the decks for giving citizenship to the religiously persecuted minorities from Bangladesh, Pakistan and Afghanistan.
However, Trinamool's Hooghly district president Dilip Yadav said the BJP always wants people to be in difficulty and danger.
"BJP is the biggest danger for the country. They will either block roads, or vandalise or create disturbances," he said.
At Buniadpur, police put up barricades to block the BJP marchers which led to a scuffle between the two, leading to tension in the area.
( With inputs from IANS )