We present GuidaPA, a privacy-preserving chatbot for the Italian Public Administration (PA) trained via Federated Learning (FL) on documentation from two national PA platforms, SIGESON and SIDFORS. Our corpus includes approximately 8 pages of SIGESON manuals and 31 pages of SIDFORS manuals/FAQs; while this study uses public documentation as a safe proxy, the intended deployment extends to restricted internal sources (e.g., tickets, officer manuals, database extracts) that can not be centrally pooled due to regulatory and organizational constraints. GuidaPA integrates role-based access control, secure client-side preprocessing, explicit monitoring of non-IID effects, and parameter-efficient federated fine-tuning of large language models. Using QLoRA (4-bit) over 15 federated rounds with an 80/20 train-test split per client, we evaluate answer quality with ROUGE, BLEU-4, and METEOR. The best federated model achieves ROUGE-1/2/L of 61.10/55.77/59.44, BLEU-4 of 45.02, and METEOR of 63.94-close to private centralized fine-tuning while keeping data on-site. Compared to the general-purpose baseline, domain fine-tuning improves ROUGE-1 from 41.45 to 62.18 and BLEU-4 from 26.97 to 50.90. Overall, the results indicate that FL can deliver high-quality conversational AI for public services without centralized data sharing