The relationship between the burglars and the Committee to Reelect the President was that the committee in essence ordered the burglary.
In the run-up to the 1972 presidential election, there were some worries among Nixon’s people that the president would not be able to win the election without taking drastic measures. This was somewhat astonishing since the election ended in a landslide for Nixon. However, the members of the CRP were worried. One of the members, G. Gordon Liddy, proposed a campaign intelligence program that would include spying on the Democratic Party. The leadership of the CRP eventually approved a version of Liddy’s plan.
Liddy then got a man named Howard Hunt involved. Hunt was one of the “plumbers” who had been assembled to stop leaks of information deemed harmful to the president. Their activities included such things as burglarizing an office to try to find damaging information about a person who was “leaking” documents. Hunt and Liddy organized the burglary at the Watergate which was to end up creating the whole scandal.
The burglars, then, were ordered to do the burglary by people involved in the CRP.