If, as I suspect, this expression is used in a document from Spain, it refers to examining or taking testimony from the parties to a civil proceeding during trial.

If you need more detail (or more vocabulary), you can see the Spanish Civil Procedure Act 1/2000 (Ley de Enjuiciamiento Civil), Capítulo VI, Sección I "Del Interrogatorio de las Partes":

http://noticias.juridicas.com/base_datos/Privado/l1-2000.l2t...


--------------------------------------------------
Note added at 2 hrs (2009-12-15 07:59:07 GMT)
--------------------------------------------------

Although perhaps this should be verified by a Colombian colleague, it appears that the expression "interrogatorios de parte" means the same in Colombia as in Spain (testimony of the parties given in open court). Here are some examples of how the expression is used in Colombian court judgments:

TRIBUNAL SUPERIOR DEL DISTRITO JUDICIAL
A la razón anterior, está la de que los argumentos que fueron expuestos en los interrogatorios de parte que rindieron las demandantes en el proceso y con ...
www.ramajudicial.gov.co/.../SENTENCIA JURISDICCION VOL. 200...

CORTE SUPREMA DE JUSTICIA
Señala como pruebas equivocadamente apreciadas, la carta de terminación del contrato, los interrogatorios de parte del actor y del representante legal de la ...
www.notinet.com.co/serverfiles/servicios/.../csj12077-00.ht...

Sobre tales documentos hicieron expresa referencia las partes del proceso, en los respectivos interrogatorios de parte. (Folios 0308-0309 del expediente). ...
www.sic.gov.co/Normatividad/.../Res_10529_2005.php

... se ocupó el Tribunal de resumir los diferentes medios de prueba obrantes en el proceso, específicamente los interrogatorios de parte absueltos por las ...
www.superservicios.gov.co/basedoc/corte_suprema.shtml?x...

Aunque no consta en el contrato de trabajo, con los interrogatorios de parte practicados al demandante y al representante legal de la empresa demandada en ...
www.derechodeautor.gov.co/.../Sentencia del 27 de abril de ...



--------------------------------------------------
Note added at 8 days (2009-12-23 08:59:43 GMT) Post-grading
--------------------------------------------------

I would like to offer a comment with respect to the answer "requesting interrogatories of the party". In this case, "interrogatorio de parte" and "interrogatories requested of a party (during discovery)" are false friends. In the Spanish system of civil procedure (in Spain, and in other Latin American countries, according to many colleagues with whom I have discussed this) there is really no pretrial "discovery" as conducted in Anglo-American jurisdictions. Civil procedure in Spanish-speaking countries is not "party driven." There is no real pretrial out-of-court examination of evidence, and a party cannot request pretrial interrogatories and an exchange of documents, or take depositions from witnesses, as is possible in the US during the pretrial discovery phase of the proceedings. To do so would contravene one of the main principles of Spanish civil procedure (the "principio de inmediación") which requires the intervention ("inmediación") of a judge during the examination of evidence and, indeed, during all stages of the proceedings. Thus in Spanish "interrogatorio de parte" is taking testimony from (or) examining a party in court in the presence of the judge, while in English, and within the context of Anglo-American civil procedure "requesting interrogatories" refers to one party asking the other party to answer a set of written questions (called "interrogatories") prior to trial in what in the US is called "discovery" (and now, with the Civil Procedure reform, is called "disclosure" in England and Wales).