Not all API documents related to relief systems are standards but the 5th edition, April 1998 is actually titled API Standard 2000. Further information about why this document is titled as a standard and what that means can be found in the Special Notes section in the front of the document.
Certainly you need to be clear about what type of vessel and relief device to which you are referring but if API 2000 applies, there is a section (4.5.2 Installation of Pressure and Vacuum Relief Devices) that addresses block valves installed between the tank and the pressure or vacuum relief device.
As far as whether there are other standards that might prohibit the use of block valves, I have known some companies' standards that do not allow the use of block valves except for the 3way type. So as Montemayor indicates, you need to check any local requirements.
In regards to atmospheric or low pressure storage tanks, I would caution you that you have very little room for error due to the low pressure rating of those tanks and you should thoroughly consider the risks versus the benefits of providing isolation for the tank relief device. To impress a point, I have known tanks to have been taken out of service, their vacuum relief valves removed for servicing and the nozzle to be covered with plastic sheeting to prevent anything from getting into the tank. No thicker than what the plastic sheeting was, it was sufficiently strong enough to result in damage to the tank as it went to an inbreathing condition.
Now having taken a second look at your post, I have concerns about what you seem to imply. Does LOTO refer to Lock Out / Tag Out? Why would you want to isolate the tank's relief device when trying to unplug a line between the tank and the end user?