Ohio - Is it a loan or a gift?

Unbeknownst to my brother, his girlfriend kept a journal of money she now claims he owes her. Let me clairify. For example, if he doesn't have money for a movie ticket, she'll pay and then write the ammount down in this journal. Or, she'd spend $30.00 on groceries and write down, "owes $15.00 for groceres" and the date. However, when he bought groceries, he never asked her to split it. Does she have any legal claim to this money, since they were in a relationship for over three years and were living together the last year? If so, can he collect money from her? He knows he's forked over three thousand dollars to her during the course of their relationship because he always wrote her a check.

I recently sat in a court room during a trial on almost the same identical thing. A handwritten log not signed or noterized is not acceptable, However the Judge did take all receipts that were valid and allowed that for the claim.

Hope this helps
Groveport (ohio)