Unfortunately right now, No there is not an official source with a release date for the second season and as a result there is no exact date (as of yet).
A post on Cross Map, an unofficial source, (By Yumi Redfield On January 17, 2016) explains that:
There have been rumors claiming that Attack on Titan season 2 will be released in February, but it is already mid-January, and still no confirmation for an Attack on Titan season 2 has been released by Tetsuro Araki, the Attack on Titan director.
A given (unofficial) explanation is:
The major reason why Attack on Titan season 2 has taken years to release is because of the (very well thought of) agreement between Attack on Titan manga writer Hajime Isayama and the Attack on Titan anime director Tetsuro Araki that the manga should always be 4 arcs ahead of the anime adaptation. This agreement would ensure that the anime would not get ahead of the manga and end up deviating too much from the source material.
This answer is based on sources available on 19/01/2016 at 17:10pm BST.