What is the responsability the House of Representatives has sole authority to do if an official has committed a crime?

Answer 1

A watered-down version of the impeachment process:

- Somebody (Representative or not) presents a case to the House of Representatives that an official should be impeached

- The HoR votes (with a simple majority holding the decision) whether to impeach the official

- The Senators hear the case against the official, with the Senate acting as a courtroom, the Chief Justice presiding over the whole thing, and Representatives acting as prosecutors

- Senators vote whether or not to convict the official, with a 2/3 majority needed for a conviction

...To answer your question simply, they are the ones who actually impeach the official.

Answer 2

The House can pass a bill of impreachement which lists the charges against them. This forces the Senate to hold a trial based on the charges and if 2/3 of the Senators find the person guilty , he is dismissed from office. He can then be indicted like a regular citizen and be tried in court.