The Prime Minister was asked about the threat to A&E services in Dewsbury and Huddersfield as she campaigned today in Thornhill.
The future of NHS services has been a key theme of Labour's campaign to hand on to marginal West Yorkshire seats including Dewsbury and Batley and Spen.
Mrs May said: ""My understanding is that there is some scaremongering going on about what's going to happen.
"I suggest people don't listen to that scaremongering but they look at the party, the Conservative Party, that is putting more funding into the NHS and that is ensuring the NHS at the local level is actually driven by local people and what local people need."
Paula Sherriff, who is defending the Dewsbury seat for Labour, claimed Mrs May's comments showed "an astounding ignorance" of the problems facing the NHS in the area.
She said: "Perhaps it’s unsurprising - Theresa May refused my invitations to visit and see the challenges here for herself, whilst [Conservative candidate] Beth Prescott has failed to attend a single one of the public meetings on the reconfiguration of Dewsbury’s hospital services.
"The truth is that whilst our hospital staff work incredibly hard, Dewsbury has suffered sustained and serious staffing shortages. This is the worrying backdrop to the very real plans to downgrade Dewsbury’s A&E services.
"Taken together with the cuts at Huddersfield Royal Infirmary, the whole of Kirklees stands to be left without full A&E facilities, putting services that are already at breaking point under even greater pressure.
"Only Labour has proposed to halt the Tories chaotic hospitals programme."
Ms Sherriff took the Dewsbury seat from the Conservatives in 2015 with a majority of 1,451.