In the beginning Park is in bed with creepy mustache guy who she later gives the cold shoulder to when he grins and says hi in the mess.
And in the end she's with Greer.. so it seems this is why Park is a lot more chilled out that everyone else!
There's also a webisode which features Park talking about her boyfriend on Earth, and then during it some other guy (just a random background guy in military uniform) shows up and the two of them make out.
Personally, I'm a bit disappointed they didn't show this side of Park more often. Not that I object to her eventually settling down and developing a relationship with Greer, but being the ship's slut (for lack of better term) would have been an interesting direction for the character, IMO.