Read the excerpt from The Dark Game.

On January 16, 1917, in a clear attempt to convince the Mexican government to help Germany in the war, Arthur Zimmermann, the German foreign secretary, sent a telegram to Count von Bernstorff, the German ambassador in Washington. The foreign secretary wanted to be certain that this message reached von Bernstorff, so he made arrangements for it to be carried aboard a U-boat to Sweden and from there to Washington through diplomatic channels.
As luck would have it, the departure of the sub was delayed. Impatient, Zimmermann turned to his second option: sending the message to his ambassador through the U. S. State Department. Although Wilson considered the United States to be neutral, he allowed messages to be sent to von Bernstorff via the State Department as a courtesy. The telegram sent, Zimmermann waited for a reply. What Zimmermann didn't know was that the British were doing a thorough job of intercepting German wireless transmissions.

Why did Zimmermann choose to send the message through the U. S. State Department?

The German U-boat was grounded because it needed repairs.
The Americans planned to enter the war and side with the Germans.
The content of the message was extraordinarily important.
The safest way of transmitting messages was by telegram.