The answer to this is still unclear. Stephenie Meyer has said that she would use the movies to clear some things up, as in, questions that fans keep asking. In the books, Jasper never said anything being in a relationship with Maria, other then helping her with the newborn army. In the movie, however, we see them kissing and he states "I thought what we had was love".
In my own personal opinion, this says that, yes, they were in some sort of relationship, but Maria had ulterior motives. She used Jasper's age and inexperience with women to make it seem as though they were in a relationship, but used it for her own ill gain. (Just like Victoria and Riley.)
However, if you mean intimate as in a sexual relationship, Jasper has never said, so we have no idea. Remember that he was a very proper Southern boy, so I think we can safely assume that his virtue went to Alice.
Maria
Maria from texas
"Intimate" commonly means a consummated sexual relationship.
It all depends on how intimate the relationship is. In an intimate relationship it is fine.
You can read about Jasper's story in Eclipse.
A vampire named Maria turned Jasper for her vampire army during the time of the Texas Civil War.He was bit by Maria.
maria
1863 by Maria
A vampire named Maria; Jasper's story is in Eclipse, the chapter named "Newborn"
The term for an intimate relationship between two different species is called interspecies relationship.
He was changed by a vampire named Maria.
Jasper HALE was 20 years old when he was turned into a vampire by Maria in Texas.