"The mother of the deceased person had earlier given some statement before some television channel, but she has changed her version now. She is now saying, neither has she received any cheque nor has she been given an assurance in this regard," he told reporters in Bengaluru.
"This has been mentioned in the divisional commissioner's report.. The report is under scrutiny," he added.
The Congress had accused Mr Shah of violating the election code of conduct for allegedly giving Rs five lakh to BJP activist Raju, who was killed in Mysuru in March 2016, leading to tension in the area.
However, the BJP had denied giving any money to Raju's family.
In a tweet, BJP leader Pratap Simha rejected the claims and said Mr Shah just wanted to know how much money the party had given.
"Dear Channels, @AmitShah ji did not give any money to Raju's family, he only asked how much compensation we gave on behalf of the party n it was 5 lakh," he had tweeted.
Mr Kumar further said as many as 1,361 teams had been formed to implement the code.
There are 1,503 static surveillance teams, 1,542 flying squads and 1,097 check-posts to see that elections are held in free and fair manner, he added.
He released the video and posters of eminent scientist CNR Rao appealing voters to exercise their franchise in assembly polls.
The surveillance and flying squads have seized Rs 4.7 crore in cash and other types of materials worth Rs 1.21 crore since March 27 when the model code of conduct came into force.
Flying squads and teams have cumulatively removed about 12,500 wall writings, 17,600 posters and 7,700 banners from public property, Mr Kumar said.