Over 2,000 people left Mullingar Hospital's emergency department last year without finishing their treatment.
There are also significant numbers in other local hospitals.
The HSE has previously said emergency departments are for people with serious injuries or illnesses, but many others go there when they do not need to.
It said patients are treated by priority and, because of that, some patients with less serious needs may choose to get healthcare elsewhere.
New figures show 108,000 people left emergency departments around the country without finishing their treatment last year - 6.6 per cent of all patients who presented to them.
That includes over 2,200 patients in Mullingar and nearly 1,800 in Tullamore Hospital.
There were also over 1,200 in Portiuncula Hospital in Ballinasloe - and nearly 3,700 in Galway University Hospitals.
