In Ohio, "rollover" cash advances, or payday loans, as they are also
called are not permitted. The law states as a prohibition (ORC
1315.41)to "make a loan to a borrower if there exists an outstanding
loan between the check-cashing business and that borrower". My
question is this: If the borrower pays off the loan on a Wednesday and
returns the next day, Thursday, and borrows again, has sufficient time
elapsed for the loan to be legal under Ohio law?

Hi duchessmary,

It is always so much easier to find something that exists rather than
something that doesn't exist.  I have searched the Ohio Legislative
Code for hours looking for some evidence of a waiting period between
loans in Ohio and I just can't find one.

CHAPTER 1315 TRANSMITTERS OF MONEY; CHECK-CASHING BUSINESSES
CHAPTER 1321 SMALL LOANS
http://onlinedocs.andersonpublishing.com/oh/lpExt.dll?f=templates&fn=main-h.htm&cp=OAC

Sec. 1315.39.  (A) A check-cashing business licensed under sections
1315.35 to 1315.44 of the Revised Code may engage in the business of
making loans provided that each loan meets all of the following
conditions:
http://www.legislature.state.oh.us/bills.cfm?ID=125_HB_401


Following is the only mention that I found of any kind of waiting
period between loans (see # 6):

Paycheck Loan Various State Legislation
Ohio SUMMARY
1. Effective Rate: $15.00 per $100.00
2. Maximum Contract: $500.00
3. Min/Max Duration: 1 Day to 6 Months
4. Only 1 loan at a time to a customer
5. No Rollover allowed
6. Must wait 1 business day to make a new loan after payoff (Cool Off Period)
7. Full Truth in Lending Disclosure required
8. NSF Fee = $20.00 plus Bank Charge, Maximum $25.00
9. No Additional Late Fees or Interest
10. Must have a license as a Check Casher and have a minimum $100,000 net worth.
OH - This links directly to the Ohio Legislative search page. Search
on Revised Code 1321!
http://www.payday-loan-industry.com/usa-legislation.html

No mention here either:

Office of Consumer Affairs
https://www.com.state.oh.us/dfi/pub/OCA%20Payday%20Loan.pdf

Some other websites I looked at:

Number of Rollovers and Loans Permitted
http://www.consumerlaw.org/action_agenda/payday_loans/content/PaydayLoanStatsbyState2005.pdf

State comparison chart
http://www.bankrate.com/brm/news/debt/debtcreditguide/payday-chart1.asp

Ohio Legal Services:  Consumer Rights : Payday Lenders  
http://www.ohiolegalservices.org/OSLSA/PublicWeb/Library/Index/1090000/1090001/index_html#1090001

Judging from what I've seen, I would say that you should be able to
get another loan the next day (because it won't be used for paying off
your old loan which is what a "rollover" is).   If you have any
questions, please post a clarification request and wait for me to
respond before closing/rating my answer. One last thing you could do
is to call the Ohio Department of Commerce Division of Financial
Institutions Office of Consumer Affairs (1-800-750-0750), they should
be able to answer all of your questions.  Now I must go rest my poor
eyes... :)

Thank you,
hummer

I spent most of my time searching the Ohio legislation.  
Some Google search terms that I used: ohio payday loans "waiting
period" "cool off period" "cooling off period" "1 day" "24 hours" "1
business day" renew