If history does not offer evidence to support the notion that Billy the Kid and Paulita Maxwell had a relationship, it also does not offer evidence that they did not.
How do we know that Paulita was honest when she told Walter Noble Burns that she and the Kid never had a romantic relationship? Lots of women during that time tried to hide earlier amorous connections. Josie Earp sure tried to hide her relationship with Wyatt Earp. Paulita was a devout Catholic, who never divorced José Jaramillo, in spite of his abuse. Would she have admitted publicly to such a great sin—or the greater sin of having a kid out of wedlock?
Even if Paulita was never impregnated by the Kid, that does not preclude the possibility of them having a romantic relationship. Yes, historians generally agree the Kid’s main interest in Fort Sumner was Celsa Gutierrez, but his reputation was such that a relationship with her would not have prevented him from playing the field.
Billy the Kid biographer Frederick Nolan discovered gossip from that time period that the two had a romantic relationship. Apolonaria Garrett heard some of it and passed it on to her husband, Pat, although he may have dismissed the gossip. Such talk does not mean the rumor was true, but it gives weight to the possibility that the two were more than just friends…at least people who knew them believed so.