This will depend from which administration you need a certificate of no debt (certificado de deuda pendiente/o the no deuda) certificates are provided by the tax office (Agancia Tributaria) and the Social Security administration (INSS).
For a general credit check CIR (Central de Información de Riesgos) suggestion is that this is carried via the bank of Spain. Below is a link with the information in Spanish.
Application electronically with digital signature.
In person at any branch.
Bank of Spain
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