There are different statutes of fraud for different kinds of contracts. $500 is the limit for contracts to buy or sell things. You have the right statute for a loan agreement. So, gou are right on the law. Proving the loan and collecting the debt is going to be another matter.
That is very good that you researched this. Normally, an oral agreement is
a valid agreement so long as there is an offer, acceptance, and
consideration. However, considering this is CT, you may be best to speak to
a CT lawyer to ensure you have enough law to counter your ex-girlfriend's
position. However, if recognized in CT as a valid, you may have an
additional count for unjust enrichment. Though, to ascertain this and the
confirmation as whether your oral agreement meets the minimum standards in
CT, it is highly recommended to speak to a licensed CT attorney.