COLUMBUS — As real estate tycoon and reality TV star Donald Trump moves closer to the Republican presidential nomination, a new poll of Ohio voters finds support for Gov. John Kasich’s candidacy shrinking.

A Public Policy Polling survey, taken April 26-27, showed 49 percent of the state’s voters feel their governor should drop out of the race, while 38 percent said he should stay in.

Kasich, who is in a distant third in the delegate count, has been mathematically eliminated from securing a delegate majority and is staying in the race in hopes Trump fails to secure the 1,237 delegate majority required for a nomination on first ballot at the Republican National Convention in Cleveland in July.

If a candidate does not reach a majority on first ballot, the delegates would no longer be bound to a particular candidate and could vote for an alternative candidate.

Kasich has said he would not consider a vice-presidential slot on a ticket with Trump.

Though he won the state’s primary earlier this year, the poll found Kasich’s approval in the state has dropped since his presidential run began, 46 percent approving of his job as governor, and 40 percent disapproving.

A survey by PPP in March had his approval rating at 54 percent positive and 36 percent negative.

The poll also found that 49 percent of voters feel Kasich’s presidential run has caused him to pay insufficient attention to his duties as governor, while 31 percent feel he’s paying enough attention.

The poll of 799 registered voters has a margin of error of +/- 3.2 percent and was completed before U.S. Sen. Ted Cruz dropped out of the race on Tuesday.