Do I need a "certificate of no criminal record" to travel to Panama as a tourist?"

Tourist may travel to Panama for 30 days on a Tourist Card tor a Tourist Visa, (extendable to 90 days at discretion of Immigration authorities), without a criminal record check.

travel.state.gov/travel/cis_pa_tw/cis/cis_994.html
Panamanian law requires that travelers must either purchase a tourist card from the airline serving Panama or obtain a visa from a Panamanian embassy or consulate before traveling to Panama. Further information may be obtained from the Embassy of Panama, 2862 McGill Terrace NW, Washington, DC 20009, tel. (202) 483-1407, or the Panamanian consulates in Atlanta, Boston, Chicago, Honolulu, Houston, Los Angeles, Miami, New Orleans, New York, Philadelphia, San Juan, San Diego, San Francisco or Tampa.

REQUIREMENTS TO OBTAIN A VISA WITH AUTHORIZATION
FOR IMMIGRATION INTO PANAMA:
www.panaconsul.com/pages/visas_countries_canenter_visa.htm
1- TWO APPLICATION FORMS
2- TWO PHOTOGRAPHS
3- STATEMENTS FROM THE BANK
4- LETTER FROM A RESPONSIBLE PERSON IN PANAMA
5- SEND YOUR PASSPORT TOGETHER WITH A COPY OF IT
6- FEES OF £30.00 PLUS COMMUNICATIONS CHARGES IF ANY.

The Tourist Visa application does not ask about a criminal record.
www.panaconsul.com/pages/visa_form2.htm
But an immigration visa requires a Clean Criminal Record issued from your home municipality.

Authorized visas:
migracion.gob.pa/eng/servicio.php?cont=paisvisa

Authorized visas have to be requested by foreign citizens of countries that due to migratory policies require a previous authorization of the National Directorate of Migration in order to enter the country. This authorization is requested from their own country (Panama Consulate within that country), or can be requested by an interested party that resides in Panama. The applicant must comply with all the requirements demanded by law and if the visa is approved, the Panamanian Consulate within that country is notified in order to stamp the visa on the applicant’s passport so the person can travel to Panama. With this type of visa, the foreigner must specify if it is a tourist (in this case, specify the length of stay) or immigrant and thereafter Immigration decides if it is granted or not and the length of time authorized for the foreign citizen to stay in Panama.

Stamped Visa:
This visa does not require a previous authorization from the National Directorate of Immigration and Naturalization. The applicant can request it within his/her country before the Panamanian Consulate. This is a Tourist Visa and the Consul decides the length of time granted to the applicant. Only after that, the person can travel to Panama.

Tourist Card:
The citizens from countries that are allowed to travel to Panama with a tourist card do not need a visa, they only have to buy a tourist card within the airline, which cost is $5.00, fill it out it with the requested information and present it along with the passport when entering Panama. From here originates the importance of the migratory classification established by the Ministry of Foreign Affairs. If the person is a citizen from a country which is required to hold a stamped visa or a tourist card to come into Panama, this means that the person has two options, which are: to apply for a visa before the Panamanian Consulate within his country and travel with the stamped visa on his passport, or to buy the tourist card from the airline or at his arrival at the country. If the person is a citizen from a country which is classified as one that requires a stamped visa, it has no other option than to previously request a stamped visa at the Panamanian Consulate before travelling to Panama, and if the person is a citizen from a country that requires an authorized visa, the visa application requires the previous authorization of the National Directorate of Immigration and Naturalization. In all cases, it is required to comply with all the requirements to come into the country, (economic solvency, passport with a six month minimum validity and return ticket for his country.

COUNTRIES THAT NEED VISA TO ENTER PANAMA (THIS CAN BE AUTHORISED BY THE CONSULATE WITHOUT AUTHORISATION FROM IMMIGRATION AUTHORITIES IN PANAMA)
Angola Georgia Palau
Gabon Peru
Banuatu Ghana Papua - New Guinea
Botswana Kiribati Romania
Bulgaria Marshall Islands Russia
Cabo Verde Maldives Solomon Islands
Cameroon Molodva Santo Tome & Prince
Croatia Mongolia Seychelles
Comores Island Madagascal Swaziland
Congo Republic Malawl Togo
Central African Republic Mauritious Tonga
Dominican Republic Micronesia Tuvalu
Ecuador Nauru Ukraine
Fiji Occidental Samoa Vietnam
Zimbabwe