In a scene from “Fear of a Black Republican,” Catherine Davis Pleads With Republican National Committee Chairman Ken Mehlman for support of her congressional campaign. (Shamrock Stine Productions)

Kevin Williams, an earnest young white Republican living in Trenton, N.J., couldn’t believe the response he got a few years back from a county party chairman when he went to get door-hangers for a presidential election.

The chairman refused, saying there were no votes to be had in majority-black Trenton and that they didn’t want to rile up Democrats and make trouble for a Republican candidate running for reelection.

Williams persisted, and the chair grudgingly handed over the campaign literature. But the encounter left him perplexed. So Williams and his wife got out their cameras and set out to answer the question: Does the Republican Party really want more black people?

It is the opening statement in a documentary, “Fear of a Black Republican,” which is screening Thursday and Friday at the E Street Cinema.

Williams, who serves as the narrator of the film, poses the question to various Republican political leaders, including former Republican National Committee chairmen Michael Steele and Ken Mehlman, and current presidential contenders Mitt Romney and Newt Gingrich.

Of course, everyone says, it’s important that the party try to win over black voters. Williams said he began the project wondering whether racism was at the root of the party’s relationship with African American voters but came to the conclusion that perhaps the party has decided it’s a hopeless cause.

“What we really found was that they have led themselves to believe, ‘They will never vote for us,’ so they don’t even try. It’s a self-fulfilling prophecy,” Williams said in an interview.

The documentary covers the period that includes the 2008 presidential election, but recent events in the current Republican nominating contest suggest little has changed with regard to the party’s struggle to connect with African American voters.

Early on in this year’s primary season, Gingrich was criticized for using what some people deemed racially loaded language and sparred at a debate with Fox commentator Juan Williams over the candidate’s labeling of President Obama as the “food stamp president.” Herman Cain, an Atlanta businessman who is black, was at one point the most popular candidate in the Republican field among tea party activists, but he drew ire for behavior that some political and cultural critics thought was demeaning to black people.

Polls conducted during the primary season have shown black voters continue to overwhelmingly support Obama.

Kevin Williams, who shares cinematography credit with his friend Jeffrey Metzner, financed the project with his wife out of their own pockets. He and his crew worked on the film for more than six years, and he estimates it cost just under $600,000 to make. He is also paying for the cost of screening “Fear of a Black Republican,” which debuted last summer and has been shown in a dozen cities around the country.

The title of the film is an ode to the rap group Public Enemy’s album “Fear of a Black Planet.” Williams, who studied film in college, has also made a couple of short features and music videos. He is a stay-at-home father for part of the week while his wife works in the fashion industry in New York.

At 43, Williams, who grew up in Trenton, sounds like an old-school Northeastern Republican. His parents were Democrats. “My mom was a very big Kennedy Democrat, and my dad was an FDR man,” he said. He gravitated to the GOP, he said, because “their core beliefs are more in line with what I believe in: entre­pre­neur­ship, personal responsibility, small government.” On social issues he describes himself as moderate.

The film traces the party’s history with African American voters, who favored it when it was the party of Abraham Lincoln, who signed the Emancipation Proclamation, ending slavery. It also discusses the party’s more recent history, including the “Southern strategy,” in which the party exploited racial angst of white working-class voters.

Williams looks at the quixotic quest in 2006 by Catherine Davis, a black Republican, to win a congressional seat in suburban Atlanta. Not only is she not taken seriously by black voters, but she is brought to tears after she is snubbed at a GOP rally by state party leaders.

Williams said although he believes black people have negative attitudes about his party, he has found that many are at least willing to have a conversation.

Williams said he hoped his film would encourage his fellow party members to realize that they’re never going to attract black voters if they keep ignoring them.

“If my party is so sick and tired of being called racist, well, here’s your chance to prove them wrong,” he said. “Go to Trenton, go to Philly, D.C. There’s no reason why we can’t go to black areas to campaign and give some cover to black Republicans who are out there.”