Seven feet.
min space for head room is 7 foot 6 inches min for finished habitable space
You will need at the very minimum 6’8" or 80" to install drop ceiling. Of course, the more headroom the better, but you should meet the same requirements as a standard door.
The International Residential Code states that habitable spaces in basements shall have a ceiling height of 7’-0". Bathrooms are required to have a minimum ceiling height of 6’-8" at the fixtures (note: there are specific clearance floor areas that this is applicable to).
Often local jurisdictions have more stringent height requirements than the IRC.
Based on recent CA residential code changes, the minimum ceiling height has been reduced to 6ft 8in. The exception for allowing beams, girders, ducts or other obstructions to project to within 6ft 4in of the finished floor includes now basement with habitable space. It is generally recommended to keep it 7 min.
The minimum head room should be 7 foot 6 inches.