While there may not have been any confirmed combat deaths in Japan proper, there were clashes with Japanese holdouts for several years after the war ended, including Amercian combat deaths. From the link:

February 22, 1946 - Lubang island Allied casualties in a post WWII battle
Intense fighting developed on February 22, 1946 when troops encountered 30 Japanese. Eight Allied troops were killed, including 2 Filipinos. The Filipino and Americans sent for an additional 20,000 rounds of small arm ammunition, but not future battles occurred of this magnitude. In early April, 41 members of the Japanese garrison on Lubang island came out of the jungle, unaware that the war had ended.

March 1947 - Ei Yamaguchi's Band Attacks US Marines
Peleliu is a small six mile long by three mile wide island. It was originally secured by American Marines in November of 1944 after fierce fighting. A band of 33 Japanese soldiers renews fighting on the island by attacking a Marine patrol with hand grenades. At that time, only 150 Marines were stationed on the island, with 35 dependents. Reinforcement were called in to hunt down the hideouts.American patrols with a Japanese Admiral sent to convince the troops that the war was indeed over finally convinced the holdouts to come out peacefully.

Likewise, in both countries, a considerable number of Allied personnel were killed during the occupation by criminals, land mines, and assorted accidents.