THE LEGISLATURE TOOK another step Tuesday towards advancing a bill that would crack down on handheld cellphone use by drivers.

In a poll set to end Wednesday afternoon, members of the Transportation Committee have been asked to weigh in on two similar proposals filed by members of the House and Senate that would basically bar motorists from using their phones to talk or peruse social media while behind the wheel.

In prior sessions, proposals to tighten the rules around the dangerous and distracting behavior have passed the Senate and received initial approval in the House, but none have reached the governor’s desk. It is one of the early high-profile pieces of legislation this session, and Gov. Charlie Baker has sought similar changes through his broader road safety bill.

The bills will move out of the Transportation Committee at the conclusion of the poll, putting them one step closer to votes in the two legislative chambers.

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Neither of the bills address what has been a major sticking point for some lawmakers and advocates who believe the so-called hands-free bills should also seek to curb racial profiling by police.

With both Transportation Committee chairmen – Rep. William Straus of Mattapoisett and Sen. Joseph Boncore of Winthrop – recommending approval of the bills, they are likely to receive favorable recommendations by the committee members.

One bill was filed by Straus, and the other, which was amended slightly by the committee, was sponsored by Senate Majority Leader Cindy Creem. The Creem bill specifies an escalating scale of fines that would go from $100 for a first offense to $500 for a third or subsequent offense.

Straus’s bill specifically bans drivers from using a handheld phone to carry on a conversation, take photos, or access social media, while Creem’s bill bars drivers from touching or holding phones except to activate, deactivate, or “initiate a feature of function.” Both bills provide an exception for phone use in the case of emergencies.

Lawmakers outlawed texting while driving in 2010, but pretty much immediately afterwards police and others complained that the anti-texting law was difficult to enforce.

The committee action is occurring just before the House and Senate take up the annual budget bills – an intensive process that tends to put other legislative priorities on hold. The House Ways and Means Committee plans to vote on its budget proposal Wednesday.