A landlord should do everything they can to prevent and get rid of mice and other pests and that includes either getting rid of the mice themselves or hiring a pest control company to do the job.
But I don't think any law would force them to pay for the pest control service if the tenant hires the pest control company without talking to the landlord first.
If you hired the pest control company without first contacting the landlord in advance and trying to get them to get rid of the mice or other pests then the bill for the pest control company would likely be your responsibility.
Always contact your landlord first to see if they will get rid of the mice or other pests.
If the landlord doesn't do anything about the mice or other pests after you tell the landlord about it and then you hire a pest control company then the landlord may be responsible for the bill of the pest control company.