Ghana was once hailed as a regional growth model but has lost its lustre after taking on too much debt.
Akufo-Addo accused the ruling party of fomenting violence as police turn a blind eye, casting doubt on the country's reputation as beacon of democracy in Africa.
"We're certainly in a very critical space," Akufo-Addo told reporters at his house in Ghana's capital Accra after a rally.
"It's important that these acts of violence being perpetrated by operatives of the ruling party are dealt with according to the rule of law," Akufo-Addo said.
"We have definite reservations about the neutrality of the police."
Fears about the erosion of Ghana's democracy have dominated the presidential campaign, with claims of voter intimidation and questions over independence of the Electoral Commission.
An exporter of gold, cocoa and oil, the West African country was once hailed as a regional growth model but has lost its lustre after taking on too much debt.
During the bitter presidential campaign, New Patriotic Party (NPP) candidate Akufo-Addo criticised incumbent John Mahama for mismanaging the economy and allowing corruption to flourish.
National Democratic Congress (NDC) leader Mahama has painted a radically different picture of Ghana, touting his government as an example of fiscal discipline and promising that tackling corruption will be one of his priorities if reelected.
If neither the NDC or NPP win more than 50 percent of votes, a presidential run-off will take place later in December.
Elections in Ghana are often down to the wire -- Akufo-Addo has lost narrowly twice before -- but the economic crisis may swing voters his way.
At a final NPP rally in Accra, there were echoes of Barack Obama's seminal 2008 campaign, with jubilant supporters waving huge blue "hope" flags and blowing plastic horns.
Many in the crowd said they were "suffering" without jobs, describing Akufo-Addo as an "incorruptible" leader who could restore the economy and help Ghana compete with regional star Ivory Coast.
"The winds of change are blowing the whole of Africa, all the corrupt leaders are being taken away," said 40-year-old Bernard Owusu.
"It happened in Gambia, it happened in Nigeria, and other parts of Africa, and it's time for Ghana."
When Akufo-Addo took the stage, the crowd unleashed an earsplitting roar as fireworks popped overheard.
"NDC is corrupt," said Margaret Darkwah, a 55-year-old decked out head-to-toe in NPP paraphernalia.
"So we are throwing them out."
Mahama has worked to take the high road in the campaign, playing the part of statesman.
"Let's continue to ignore all forms of provocation," Mahama said in a statement on Twitter over the weekend, urging Ghana to vote and peacefully "wait for the results."
Mahama studded his campaign with announcements of new infrastructure works and "cash donations", according to a October report by the Ghana Center for Democratic Development, a non-profit organisation based in Accra.
In a recent survey, local pollster Ben Ephson predicted Mahama will win in the first round with 52 percent of the votes, although others have predicted a NPP victory.
Mahama will hold a rally Monday in Accra before heading to his hometown of Bole in the north to cast his ballot.
Akufo-Addo will go vote in the eastern town of Kibi, with the election results expected to be announced in Accra within a couple of days.
Sporadic violence, spurred on by so-called "macho men" -- party-affiliated gangs -- may break out in some areas, but nationwide violence is unlikely.
Still, it's a "dangerous" time, Akufo-Addo told reporters at his house.
"The consequences of the election on Wednesday are really, really serious for the future of our country."