Haddish was back onstage just hours after she was picked up by Beverly Hills police on Friday morning.
Police found Haddish while responding to a call about a car stopped in the middle of a busy street in Beverly Hills.
The law, named "Bentley's Law," went into effect Friday.
“The consequences can be devastating. Do not risk your life or your career," said the email to Los Angeles police officers.
The husband of House Speaker Nancy Pelosi was charged with driving under the influence after a May car crash in California.
Apopka police officer Oscar Mayorga was seen slurring his speech in a bodycam video on Monday.
The House speaker's husband was arrested last month after allegedly driving under the influence of alcohol.
The House Speaker's husband, Paul Pelosi, was involved in a collision in Napa County, authorities said.
A representative for the House speaker's office called it a "private matter" and said she was on the East Coast when the incident occurred.
Police say an intoxicated driver rammed his truck into parked cars in southern Germany, shoving the vehicles against buildings and causing some of them to catch fire.