その政治家は事件と関係があるようだ。

English Translation

The statesman seems to have links to the matter.

The nuance of 事件 doesn’t match “the matter” in English. We use 事件 specifically for criminal cases, unethical incidents, scandals etc. The “matter” can include these negative cases, but the “matter” can also mean “a certain social agenda” in a variety of contexts.

I would propose:

その政治家は、その事柄(ことがら)と関係があるようだ。(事柄 is closer to "content of a certain agenda)

その政治家は、その問題(もんだい)と関係があるようだ。(問題 is closer to “a problem/issue” required to be solved)