It is unlikely that constipation by itself can cause such an infection. I have never heard of such as case.
However if there is a GI source of infection leaking into the bloodstream, this is a possible cause.
Most cases of meningitis occur when colonization by potential pathogens is followed by mucosal invasion of the nasopharynx. However, some patients develop disease by direct extension of bacteria across a skull fracture in the area of the cribriform plate. Other patients develop meningitis following systemic bacteremia, as with endocarditis or a urinary tract infection. Other predisposing conditions include asplenia, complement deficiency, corticosteroid excess, and HIV infection.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Thanks,
Kevin, M.D.
Bibliography
Fekete. Clinical features of acute bacterial meningitis. UptoDate, 2004,