Tenant trying to make the rules

[Jamison Svo]

So I've got a weird situation I'm a landlord in Ohio.

I had a lease with my tenant for 1 yr 3/2018 -3/2019.  After that the tenant went month to month from 3/2019 till 3/2020.

On 1/31/2020 I served a 30 day termination of month to month lease. Over the next couple of weeks we offered several different options for new lease. The tenant refused all of these options.

The lease terminated on 3/1/2020

On 3/6 he tried to pay the old month to month rate. We promptly refunded his money stating he had no signed lease with us.

Today we filed the 3 day notice to leave.

The tenant keeps saying there's a statute that says because we offered him a lease renewal (even though he refused to sign any of them) that he has 30 days to refuse it and is therefore still under the old lease and only wants to pay for March but leave by April 30th. 

I feel like I'm taking crazy pills

Anyone else run into this.

Thanks guys & gals

Side notes:

Old lease was 575/ Month

New lease Offered at 600/month.

600/ month lease offer was retracted out of possible utility issues (duplex utilities not split)

whole house lease was offered for 1200/month with option to sublet upstairs apt.

Tenant was told we would need a lease signed by 3/4/2020 or vacate premises by 3/8/2020 12:00am