Florida does not require that you file form HSMV 82050 in order to avoid liability after the sale of a vehicle, but it is a good idea to do so and to meet the deadline of doing so within thirty days of the sale:
Quote Quoting Florida Statutes, Sec. 319.22(2) Transfer of title.
(2)

(a) An owner or coowner who has made a bona fide sale or transfer of a motor vehicle or mobile home and has delivered possession thereof to a purchaser shall not, by reason of any of the provisions of this chapter, be deemed the owner or coowner of such vehicle or mobile home so as to be subject to civil liability for the operation of such vehicle or mobile home thereafter by another when such owner or coowner has fulfilled either of the following requirements:

1. When such owner or coowner has made proper endorsement and delivery of the certificate of title as provided by this chapter. Proper endorsement shall be:

a. When a motor vehicle or mobile home is registered in the names of two or more persons as coowners in the alternative by the use of the word “or,” such vehicle shall be held in joint tenancy. Each coowner shall be deemed to have granted to the other coowner the absolute right to dispose of the title and interest in the vehicle or mobile home, and the signature of any coowner shall constitute proper endorsement. Upon the death of a coowner, the interest of the decedent shall pass to the survivor as though title or interest in the vehicle or mobile home was held in joint tenancy. This provision shall apply even if the coowners are husband and wife.

b. When a vehicle or mobile home is registered in the names of two or more persons as coowners in the conjunctive by the use of the word “and,” the signature of each coowner or his or her personal representative shall be required to transfer title to the vehicle or mobile home.
The department shall adopt suitable language to appear upon the certificate of title to effectuate the manner in which the interest in or title to the motor vehicle or mobile home is held.

2.When such owner or coowner has delivered to the department, or placed in the United States mail, addressed to the department, either the certificate of title properly endorsed or a notice in the form prescribed by the department. In addition to the information required by the department under this subparagraph, the notice must also contain the information required under paragraph (b) when the title being transferred is to a motor vehicle.

(b) An owner or coowner who has made a bona fide sale or transfer of a motor vehicle and has delivered possession thereof to a purchaser shall notify the department within 30 days after the sale or transfer in the form prescribed by the department. Notice by such owner or coowner under this paragraph shall satisfy the notice requirement under subparagraph (a)2. for limitation of liability under paragraph (a). The notification shall include the vehicle identification number and the buyer’s full first name, middle initial, last name, and personal or business identification, which may include, but need not be limited to, a driver’s license number, Florida identification card number, or federal employer identification number, and any information required by the department. This paragraph shall not apply to any transfer or sale to or by a licensed motor vehicle dealer or to an insurer who has taken possession or is taking possession of the vehicle or the title thereto pursuant to a policy of insurance.

(c) The department shall inform the motor vehicle owner or coowner of the requirements of this subsection with the issuance of each certificate of title to a motor vehicle. The information may be printed on the certificate of title or on a separate form that is included with the certificate.

You have stated that you made proper endorsement and delivery of the title. The difficulty you are facing is that you have not retained a copy of the title, and there is thus some question as to whether the car was in fact conveyed to a buyer.

If the car was purchased with a traceable means of payment (e.g., a check), it may be possible to get the buyer's information through your bank records (i.e., their record of your deposit of the check). If the person driving the car claims he was test driving the car, odds are the police have either investigated that complaint and identified the seller, or have determined it to be false (based upon no reports of a stolen or missing car, and the driver's inability to provide any information about the seller's identity or location). I would expect the conclusions of the police to be reflected in their report.

Do you still have the license plate from the vehicle you sold? Did you transfer it to another vehicle?