Dean Martin was a happily married man and father. I have never heard that they ever had any kind of sexual relationship. The "closeness" they displayed was purely for business reasons. They had a successful partnership that worked and made them both wealthy.
"The Dean Martin Show, also known as The Dean Martin Comedy Hour, first premiered on September 16, 1965. The show ran for 9 seasons until 1974 and was hosted by Dean Martin and was a variety show that had many different celebrities doing improv."
The Dean Martin Show also known as The Dean Martin Variety Show is a TV variety-comedy series that ran from 1965 to 1974 for 264 episodes. It was broadcast by NBC and hosted by crooner Dean Martin. The theme song to the series was his 1964 hit "Everybody Loves Somebody."