• Statement (I) is Correct: Methenamine (hexamethylenetetramine) is an oral urinary tract antiseptic utilized in small animals (dogs and cats) for the long-term prophylactic management and treatment of recurrent, chronic lower urinary tract infections (UTIs).
• Statement (II) is Correct: Methenamine has no direct antimicrobial activity until it reaches the acidic urinary bladder environment ($\text{pH} \lt 5.5$), where it undergoes slow hydrolytic decomposition into formaldehyde and ammonia:

Formaldehyde acts as a non-specific alkylating agent that denatures bacterial proteins and nucleic acids, preventing the development of bacterial resistance.

• Conclusion: Both Statement (I) and Statement (II) are correct (Option 1).