Tennant, in fact, would have been signed to do the shows long before he had been asked to be The Doctor, he did however get replaced in the second series of DODG by Hamish Clark. Since, by then, he was far too busy with his own police box.
Charlie Brooks from Eastenders played PC Crawford's love interest Mary Dixon's daughter on the series. This was her first job after having her daughter Kiki and she brought her to the tapings "much to everyone's delight" according to The Daily Mirror. The baby was born in December of 2004 so the tapings must have been sometime between January and April of 2005.
"Dixon of Dock Green , to be revived by Radio Four starring David Tennant who is also, of course, the next Doctor Who. Young Tennant does seem to have an odd taste for things that had their heyday before he was born. Maybe that's what coming from Paisley does for you." - The Express - May 5, 2012 - Keith Aitken
The Independent had the best headline announcing David's role in the show - which came a month after the Doctor Who announcement -