In most US states, a person finding lost property, including money, must make reasonable attempts to find the owner, and restore the property, or else turn it over to the police so that they can search for the rightful owner. In some states it is required that the police or some other authority be notified. If, after a period defined by law (and which varies significantly by jurisdiction) the finder may be able to claim the property and obtain title to it, if proper procedures are followed.
Stolen property with an identifiable owner, however, will usually be returned to the lawful owner.
Fimndlaw's article "Do You Have to Return Found Money? " states:
Under several states' laws, if you find more than a certain amount of money, you are required to take it to the police if you can't identify the owner and return it yourself. The amount of money that requires you to do so varies by state. For example, in New York, it is $20, while in California it is $100. Typically, the laws will honor finder’s keepers. If after turning in cash or lost property to the police and the true owner cannot be found, after a period of time, the finder may become the keeper. In some places however, depending on the value of the item, there may be certain restrictions.
If you find lost property that is valuable or clearly not abandoned, keeping it could result in you facing theft charges. So like the rule of the playground requiring you to loudly announce finder's keepers, if you find lost property (including cash) in the real world, you need to let the authorities know, especially if you want to legally keep it.
For example, in Maryland general Code § 7-104(d) (theft) provides that:
(d) A person may not obtain control over property knowing that the property was lost, mislaid, or was delivered under a mistake as to the identity of the recipient or nature or amount of the property, if the person:
(d) (1) knows or learns the identity of the owner or knows, is aware of, or learns of a reasonable method of identifying the owner;
(d) (2) fails to take reasonable measures to restore the property to the owner; and
(d) (3) intends to deprive the owner permanently of the use or benefit of the property when the person obtains the property or at a later time.
There is also the special purpose law Code § 13-702 which provides:
(a) Disposition.- Any currency or item of tangible personal property lost or abandoned on property owned, leased, operated by, or under the control of the University System of Maryland and unclaimed for 1 year becomes the property of the University System of Maryland and the Board of Regents may establish procedures to dispose of the property in the best interests of the State.
(b) Funds derived under section.- After deducting any cost incurred in disposing of the property, any funds derived under this section shall be deposited in the General Fund of the State.
(c) Claim of finder.- Notwithstanding subsection (a) of this section, any person who finds any currency or item of tangible personal property lost or abandoned on property owned, leased, operated by, or under the control of the University System of Maryland and brings the currency or item to the University in order that the University can find the true owner, has a superior claim as to the University to the unclaimed currency or item, if the claim is preserved within 30 days following the 1-year period in subsection (a) of this section.
Various local jurisdictions seem to have local laws with provisions somewhat similar to § 13-702.
An Article in the Baltimore Sun "Discovering lost property not always as simple as 'finders, keepers' reads, in part:
"Finders, keepers" doesn't always cut it for lost or mislaid property. So before you start spending the $10,000 you found in the zipper compartment of a handbag you bought at a yard sale, you should know that Maryland law puts a burden on the finder to try to locate the owner before claiming the find.
Some finders end up richer only in experience. A Virginia woman who claimed she bought a Renoir painting at a flea market lost title in a court case early this year. The painting, valued at between $22,000 and $100,000, had been stolen from the Baltimore Museum of Art in 1951. A judge awarded title to the museum.