Short answer. Presumptively yes, up to the height the two buildings share. The law presumes a party wall in dividing walls of adjoining buildings, and in the fences and walls dividing yards or rural land. The presumption yields to a title, an exterior sign, or proof to the contrary.
What the law says
The existence of an easement of party wall is presumed, unless there is a title, or exterior sign, or proof to the contrary: (1) In dividing walls of adjoining buildings up to the point of common elevation; (2) In dividing walls of gardens or yards situated in cities, towns, or in rural communities; (3) In fences, walls and live hedges dividing rural lands.
Civil Code, Article 659 — When a Party Wall Is Presumed. Read the full provision →
Why the law presumes rather than decides
Dividing walls are old, often older than the current owners, and almost nobody has the paper showing who paid to build one. Rather than leave every such wall to be litigated from nothing, the Code supplies a starting position: it is common to both. The presumption is a rule about who must prove what, not a finding about any particular wall. A neighbour who says the wall is his alone is free to establish it, but until he does the wall is treated as shared, and he is the one carrying the burden.
The limit hidden in the first paragraph
The presumption for buildings runs only up to the point of common elevation — as high as both structures actually reach. Where one neighbour's building rises above the other's, the wall is presumed common to the shared height and the portion above it is not. This is precisely where disputes about a third storey or a raised parapet begin. It also explains why the height of each building, as built rather than as permitted, is a fact worth pinning down early with photographs and a survey.
How an exterior sign defeats it
The presumption falls to a title, or exterior sign, or proof to the contrary, and in practice the middle one does most of the work because it can be seen without documents. An exterior sign is a visible feature of the wall itself that is inconsistent with common ownership — construction features that serve one side only, or a wall that plainly stands wholly within one lot's boundary. A sign of that kind is read against the presumption without anyone producing a deed, which is why the wall should be inspected and photographed before either side starts altering it.
What being a party wall actually means for you
A party wall is not a private wall you may treat as your own. It is held in common, which means the cost of keeping it up is shared in proportion to each owner's interest, and neither neighbour may deal with it unilaterally in a way that harms the other — opening it, loading it, or demolishing it. Before doing anything to a dividing wall, look for the documents that could displace the presumption: the certificates of title, an approved subdivision plan, a relocation survey, and any building plans showing where the wall was sited.