House Majority Leader, Nancy Pelosi (Democrat), is right and House Minority Leader, Kevin McCarthy (Republican), is wrong. No vote is needed to conduct the impeachment inquiry.

https://www.latimes.com/politics/story/2019-10-07/subpoena-power-republicans-want-house-vote-impeachment-inquiry-pelosi-doesnt The House of Representatives committees have the power needed to conduct the impeachment inquiry under current house rules and no vote is necessary. At the time of the Clinton impeachment, committee chairs needed a formal vote to give them subpoena power. Since then, the rules have changed and their regular powers have been expanded, so they don't need a vote.