Tony Cook, Chelsea Schneider, and Stephanie Wang

IndyStar

Indiana voters favor Donald Trump and Hillary Clinton, but not by large margins, according to the first polls released Friday ahead of the state's critical May 3 primary.

A Fox News poll put Trump in the lead in the Republican field with 41 percent and U.S. Sen. Ted Cruz at 33 percent, with a 4 percent margin of error. Ohio Gov. John Kasich had 16 percent. Trump's lead would narrow, the poll found, if Kasich withdrew from the race.

Another poll, conducted for WTHR-13 and Howey Politics, gave Trump a smaller lead over Cruz, 37 percent to 31 percent. It also showed Kasich faring better, with 22 percent.

On the Democratic side, Clinton led U.S. Sen. Bernie Sanders 46 percent to 42 percent in the Fox poll. The WTHR/Howey Politics poll similarly had Clinton ahead of Sanders, 48 percent to 45 percent — within the margin of error.

The Fox News poll, shared with Indianapolis affiliate and IndyStar newsgathering partner Fox59, surveyed 1,205 Hoosiers across the state from Monday to Thursday. It was conducted under the joint direction of Democratic polling company Anderson Robbins Research and Republican polling company Shaw & Company Research. It had a margin of error of 4 percent on both the Republican and Democratic sides.

The WTHR/Howey Politics poll was conducted by pollster Gene Ulm of Public Opinion Strategies, surveying 500 Hoosiers over the same period. It had a margin of error of 4.3 percent on the Republican side and 4.47 percent on the Democratic side.

The polls were the first of several expected to be released before Hoosiers cast their ballots May 3. The results line up with a previous roundup of private polls by Politico that also found close contests.

Making the race perhaps even more intriguing: One in 4 Republican voters in the Fox News poll said they might still change their minds.

Fox News reported that 46 percent of self-described "very" conservative GOP primary voters prefer Cruz, while 35 percent opt for Trump. But the two Republican front-runners divide the white evangelical Christian vote nearly evenly, with 41 percent for Cruz and 39 percent for Trump.

The WTHR/Howey Politics poll also focused on how polarizing the Republican presidential race is. Trump, perhaps unsurprisingly, came out as the most controversial candidate, with both the highest favorability rating and the highest unfavorability rating from Republican voters.

Republican voters in the poll found Kasich to be the least objectionable candidate.

Among Democrats, Clinton performed better among core Democratic voters, but Sanders performed better among occasional and first-time voters, the poll found.

The tight poll results in Indiana and its sizable number of delegates make it a critical state for Trump and for efforts by Cruz and Kasich to stop him from winning the nomination outright. Trump needs to win 1,237 delegates to avoid a contested national convention in Cleveland in July. Indiana has 57 delegates at stake.

Trump, the billionaire real estate developer and reality TV star, held his first rally in the state Wednesday, drawing an estimated 4,000 people to the State Fairgrounds.

Cruz spoke Thursday to a group of 800 at an Indiana Republican Party fundraiser and is back in the Indianapolis-area Saturday, with a stop at the Oasis Diner in Plainfield and a rally at the Boone County Fairgrounds.

Both met privately with Gov. Mike Pence, who is considering whether to endorse a candidate in the race.

Kasich has several events planned in the state Tuesday.

Call IndyStar reporter Tony Cook at (317) 444-6081. Follow him on Twitter: @indystartony.