A familiar name to her, she assumed that the police would have no difficulty in instantly locating the place meant.

The haste with which the message had apparently been written, its short, sharp words, bespoke urgent need, the consciousness of imminent peril.

Plainly the writer had used the only means at hand in a hurried desperate effort to gain assistance.
"The police." The request had been for the police; then why not appeal to the police?
Why not take the note now directly to headquarters, and let them help solve its mystery?
At first West hesitated, yet a moment's thought convinced him this would be the logical course to pursue.

He could accomplish nothing alone, unguided.

His appealing to the police need not necessarily involve any disclosure relative to the Coolidge matter.