The Friesians were found in Dolwen, near Old Colwyn, on Friday after eating poisonous tree clippings dumped in a farmer's field.
North Wales Police said the culprit is described as a heavily built man, aged 50 to 60, with curly brown hair, driving a dark blue pick-up truck.
Anyone with information can call 101.
"Apparently he has been dumping clippings over past two weeks. Has to be living/working local to Colwyn Bay," Sgt Rob Taylor, of the rural crime team, tweeted on Sunday.
A post-mortem examination showed the cows, aged 16 months, died as a result of toxins found in yew and leylandii tree cuttings.
Sgt Taylor said he was "appalled" by the "atrocious" act of fly-tipping and praised the "impressive" response to his appeal for information on social media.

The firm, which sells its Chevrolet brand in India, said it would continue to provide maintenance services.
It also said that its plant in Maharashtra would continue to make cars for overseas markets, mainly central and south American regions.
GM has announced similar plans for South and East African markets as part of its global business restructuring.
GM puts $1bn India plan 'on hold'
The US carmaker said it would stop selling cars in South Africa, and sell its manufacturing business there to Isuzu Motors.
It added that Isuzu would also purchase 57.7% shareholding in its East Africa operations, assuming management control.
The firm is aiming to make significant savings through these steps.
"As a result of these actions, GM expects to realise annual savings of approximately $100m (Â£77m) and plans to take a charge of approximately $500m in the second quarter of 2017," it said in a statement.
GM's announcement comes against the backdrop of predictions that India will become the world's third biggest vehicle market by 2020.
But the firm has put faith in exports from India.
"In India, our exports have tripled over the past year, and this will remain our focus going forward," GM International president Stefan Jacoby said in a statement.
GM had planned to invest $1bn in India to boost its domestic presence, but its sales figures fell below below 1% in the year ended in March 2017.
"We determined that the increased investment required for an extensive and flexible product portfolio would not deliver a leadership position or long-term profitability in the domestic market," Mr Jacoby added.

The 18-year-old, who is the third-youngest player at Euro 2016, signs a five-year deal for an undisclosed fee.
On Monday, Dortmund signed Bayern Munich midfielder Sebastian Rode, 25.
Last week, they agreed a deal for Barcelona's Spain defender Marc Bartra, 25, after meeting his £6.25m release clause and previously signed Rennes forward Ousmane Dembele, 18.
The Rode and Dembele deals were completed for undisclosed fees.
Find all the latest football transfers on our dedicated page.
The description of a man believed to be involved in fly-tipping which left three Conwy cows dead has been released by police.
[NEXT_CONCEPT]
General Motors (GM) has announced that it will stop making cars for the Indian market by the end of 2017.
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Borussia Dortmund have made FC Nordsjaelland and Turkey winger Emre Mor their fourth summer signing.