OK, there doesn't seem to be much of a correlation. I looked at both the Dow and the Nikkei for the past 1000 calendar days.
The Nikkei rose on 359 of those days. On days that the Nikkei rose, the Dow also rose 196 times or 196/359 = 55%.
The Nikkei fell on 314 of those days. On days that the Nikkei fell, the Dow also fell on 155 of those days or 155/314 = 49%
I compared the Nikkei's performance in trading on Monday for instance while it's still Sunday night in the US, to the following US session on the same Monday, etc.