PA reports that the hip-hop star will be seen making the confession in the first episode of Channel 4 documentary series Being N-Dubz, which airs next Monday.
It is understood that the programme features a discussion which took place between Dappy and bandmate Fazer during filming after a police car passed them in a North London street.
After spotting the vehicle, Dappy is said to have remarked: "Look at the feds - they used to be a big problem to us back in the day. These lot used to chase us anywhere we used to go. They still stop and search us, but you know what - do your job."
Fazer reportedly then sang "false name and address", prompting Dappy to add: "Up to this day, we still give the wrong name and address."
A Scotland Yard spokesman told BBC News that giving false information to police is only classed as an offence if the person in question is under arrest.
The representative added: "The point of stop and search is not to ascertain your details but to undertake a search."