Crawford wrote about her friendship with the iconic singer in her memoir, A Song For You: My Life With Whitney Houston, and also spoke about it in an interview with NBC News.
The pair met in 1980 as summer camp counsellors in New Jersey.
"In the early part of that friendship, it was physical," she said. "It was during that first summer that we met, was the first time our lips touched. And it wasn't anything planned, it just happened. And it felt wonderful. And then, not long after that, we spent the night together. And that evening was the night that we touched. And that just brought us closer together."
Crawford wrote in her memoir that they "never talked about labels, like lesbian or gay", commenting: "We just lived our lives and I hope it could go on that way forever".
However, Houston ended the physical side of their relationship shortly after, apparently out of fear that it could affect both their lives. Their closeness spawned relentless speculation about Houston's sexuality over the years.
"She said that if people find out about us, they would use this against us, and back in the Eighties that's how it felt," Crawford said.
Houston eventually married R&B star Bobby Brown in 1992, before they divorced in 2006. Brown wrote in his 2008 autobiography that they got married "for all the wrong reasons" and that he felt Houston wanted to kill the scrutiny around her personal life.
"The media was accusing her of having a bisexual relationship with her assistant [Crawford]," he wrote. "In Whitney's situation, the only solution was to get married and have kids. That would kill all speculation, whether it was true or not."
Houston died in 2012 of accidental drowning in a bathtub.
A Song For You: My Life With Whitney Houston is released on 12 November.