I believe there may have been several reasons for To Kill a Mockingbird being shot in black and white rather than color. With the setting of the 1930s, an old fashioned B&W look may have been a consideration. The racial storyline and the division of blacks and whites in the South could also have been a reason. A more likely purpose was that black and white filming was much cheaper than shooting in color. Another possibility is that the TV was still primarily viewed in B&W, and this may have been a consideration for future television rights. At least the recent DVD release featured a full color photo from the film as the cover.
Director Robert Mulligan decided to film To Kill A Mockingbird (1962) in black and white, though color technology was widely used at the time. In part, the director made this decision for stylistic reasons—to create an iconic movie that made a statement that it was serious and more than just fleeting entertainment. In other words, the film was not to be enjoyed just for its color. In addition, the content of the movie lent itself to black and white film, as the film is about the divisions between the black and white segments of society in Depression Era Alabama. The black and white film allows the audience to see those divisions more clearly and to experience them as the characters in the movie are experiencing them. In addition, the use of black and white adds drama to many of the scenes, including to the courtroom scenes, in which the facial expressions of Atticus Finch (played by Gregory Peck) and Tom Robinson (played by Brock Peters) are so clear and poignant.
The film was filmed in black and white in order to give the characters the definition and not the scenery. While it is critical to the film to see the small southern town, Lee did not want the film to reduce the significance of the characters. She wanted Atticus to be viewed with the respect he need.
The other reason was the film like the town was divided in the two colors which set the tone for the story in general. It was a good choice because the film style made the film all the better and more captivating.