According to the official website, the OVA of Hyouka will be pre-aired on the official USTREAM channel on July 7th, 2012 at 24:00 Tokyo Time (stand-by at 23:50). This is the same OVA that was previously announced to be an OAD bundled with the 3rd volume of the manga planned to be released on January 13th, 2013.

Synopsis: Episode 11.5 "Motsubeki Mono wa" (Something You Should Have)
This story takes place between the 11th and 12th episodes of what you would call the main story.
An accident occurs at the public pool!? Eru, Mayaka, and the Kotenbu members run around the pool in swimsuits!?

Staff:
Plot: Honobu Yonezawa
Script: Yasuhiro Takemoto
Storyboard/Producer: Oota Rika (K-On!)
Art Director: Yukiko Horiguchi

Source: Official Website (Japanese), Kotenbu USTREAM (Japanese)

Please note, all translations made in this article are temporary and may be subjected to revision based on official updates.