RICHMOND — Police in Virginia could no longer stop cars for certain physical defects or search them based on an alleged whiff of marijuana under legislation that state Democrats are pursuing in a special General Assembly session.

The measures are part of a push in Virginia and across the country to overhaul law enforcement practices after the death of George Floyd in Minneapolis police custody in May. Backers of the changes say that under current law, police can use minor offenses as a pretext for racially motivated stops.

The state Senate’s version of the bill, passed on Friday, would prevent police from pulling over motorists for minor infractions related to the condition of their cars, such as having an unlit license plate. It would also bar police from searching cars based on a claim that they can smell marijuana. A similar House bill is expected to come to the floor of that chamber for a vote next week.

“There’s a lot of offenses that seem to result in disproportionate stops for minorities,” said Sen. Scott A. Surovell (D-Fairfax). “Now that we’ve decriminalized marijuana and said it’s only a civil infraction, law enforcement shouldn’t be able to tear your car or pockets apart [looking for it]. … You typically don’t grant the government that broad a dominion over someone’s liberty over a mere civil violation.”

Surovell and other Democrats point to the ongoing investigation of a Virginia state trooper, who was captured on video last year forcibly removing a Black man from his car, which another trooper had stopped for an expired inspection decal and then asked to search because she said she smelled marijuana. No drugs were found.

Republican legislators have opposed the measures, which they say would tie the hands of law enforcement and make the roads less safe.

Del. Robert B. Bell (R-Albemarle) said he was concerned that any evidence discovered in a traffic stop that’s deemed illegal under the proposed new standard could not be admitted in court.

“It would apply to any evidence including, for example, a body in the back seat,” Bell said.

Republican objections have not stopped the bills from advancing in the House and Senate, which both flipped to Democratic control after elections last year. Sen. L. Louise Lucas (D-Portsmouth) has sponsored the Senate bill and Del. Patrick Hope (D-Arlington) has proposed the House version.

Their bills are not identical, so any differences would have to be worked out before the legislation could head to Gov. Ralph Northam (D) for his review. Northam has been supportive of efforts to overhaul policing and criminal justice more broadly, but so far has not taken a position on the Lucas and Hope bills.

“The Governor is committed to comprehensive criminal justice and police reform,” Alena Yarmosky, a spokeswoman for Northam, said in a statement. “He is continuing to work closely with legislators on these and other measures, and will review all legislation that reaches his desk.”

Both measures would prevent police from stopping a car solely because it lacks a light on the license plate, has an excessively noisy exhaust system or has certain tinting materials on its windows. Hope’s bill has a longer list of car defects that police could not act on, including faulty brake lights, which Bell said could present a hazard to drivers. Hope was traveling Friday and not available to discuss the bill. Lucas did not respond to a request for comment.

Under both bills, officers could still cite drivers for those infractions if they had another reason to stop the vehicle.